Search: a007713 -id:a007713
|
| |
|
|
A000293
|
|
a(n) = number of solid (i.e., three-dimensional) partitions of n.
(Formerly M3392 N1371)
|
|
+10
37
|
|
|
|
1, 1, 4, 10, 26, 59, 140, 307, 684, 1464, 3122, 6500, 13426, 27248, 54804, 108802, 214071, 416849, 805124, 1541637, 2930329, 5528733, 10362312, 19295226, 35713454, 65715094, 120256653, 218893580, 396418699, 714399381, 1281403841, 2287986987, 4067428375, 7200210523, 12693890803, 22290727268, 38993410516, 67959010130, 118016656268, 204233654229, 352245710866, 605538866862, 1037668522922, 1772700955975, 3019333854177, 5127694484375, 8683676638832, 14665233966068, 24700752691832, 41495176877972, 69531305679518
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
An ordinary partition is a row of numbers in nondecreasing order whose sum is n. Here the numbers are in a three-dimensional pile, nondecreasing in the x-, y- and z-directions.
Finding a g.f. for this sequence is an unsolved problem. At first it was thought that it was given by A000294.
|
|
|
REFERENCES
|
P. A. MacMahon, Memoir on the theory of partitions of numbers - Part VI, Phil. Trans. Roal Soc., 211 (1912), 345-373.
P. A. MacMahon, Combinatory Analysis. Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 332.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Examples for n=2 and n=3.
a(2) = 4: 2; 11 where the first 1 is at the origin and the second 1 is in the x, y or z direction.
a(3) = 10: 3; 21 where the 2 is at the origin and the 1 is on the x, y or z axis; 111 (a row of 3 ones on the x, y or z axes); and three 1's with one 1 at the origin and the other two 1's on two of the three axes.
The a(1) = 1 through a(4) = 26 solid partitions, represented as chains of chains of integer partitions:
((1)) ((2)) ((3)) ((4))
((11)) ((21)) ((22))
((1)(1)) ((111)) ((31))
((1))((1)) ((2)(1)) ((211))
((11)(1)) ((1111))
((2))((1)) ((2)(2))
((1)(1)(1)) ((3)(1))
((11))((1)) ((21)(1))
((1)(1))((1)) ((11)(11))
((1))((1))((1)) ((111)(1))
((2))((2))
((3))((1))
((2)(1)(1))
((21))((1))
((11))((11))
((11)(1)(1))
((111))((1))
((2)(1))((1))
((1)(1)(1)(1))
((11)(1))((1))
((2))((1))((1))
((1)(1))((1)(1))
((1)(1)(1))((1))
((11))((1))((1))
((1)(1))((1))((1))
((1))((1))((1))((1))
(End)
|
|
|
MATHEMATICA
|
planePtns[n_]:=Join@@Table[Select[Tuples[IntegerPartitions/@ptn], And@@(GreaterEqual@@@Transpose[PadRight[#]])&], {ptn, IntegerPartitions[n]}];
solidPtns[n_]:=Join@@Table[Select[Tuples[planePtns/@y], And@@(GreaterEqual@@@Transpose[Join@@@(PadRight[#, {n, n}]&/@#)])&], {y, IntegerPartitions[n]}];
Table[Length[solidPtns[n]], {n, 10}] (* Gus Wiseman, Jan 23 2019 *)
|
|
|
CROSSREFS
|
Cf. A000041, A000219 (2-dim), A000294, A000334 (4-dim), A000390 (5-dim), A002835, A002836, A005980, A037452 (inverse Euler trans.), A080207, A007326, A000416 (6-dim), A000427 (7-dim), A179855 (8-dim).
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
More terms from the Mustonen and Rajesh article, May 02 2003
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A290353
|
|
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the k-th Euler transform of the sequence with g.f. 1+x.
|
|
+10
22
|
|
|
|
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 3, 1, 0, 1, 1, 4, 6, 5, 1, 0, 1, 1, 5, 10, 14, 7, 1, 0, 1, 1, 6, 15, 30, 27, 11, 1, 0, 1, 1, 7, 21, 55, 75, 58, 15, 1, 0, 1, 1, 8, 28, 91, 170, 206, 111, 22, 1, 0, 1, 1, 9, 36, 140, 336, 571, 518, 223, 30, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,13
|
|
|
COMMENTS
|
A(n,k) is the number of unlabeled rooted trees with exactly n leaves, all in level k. A(3,3) = 6:
: o o o o o o
: | | | / \ / \ /|\
: o o o o o o o o o o
: | / \ /|\ | | ( ) | | | |
: o o o o o o o o o o o o o o
: /|\ ( ) | | | | ( ) | | | | | | |
: o o o o o o o o o o o o o o o o o o
|
|
|
LINKS
|
B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
|
|
|
FORMULA
|
G.f. of column k=0: 1+x, of column k>0: Product_{j>0} 1/(1-x^j)^A(j,k-1).
|
|
|
EXAMPLE
|
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, 7, 8, ...
0, 1, 3, 6, 10, 15, 21, 28, 36, ...
0, 1, 5, 14, 30, 55, 91, 140, 204, ...
0, 1, 7, 27, 75, 170, 336, 602, 1002, ...
0, 1, 11, 58, 206, 571, 1337, 2772, 5244, ...
0, 1, 15, 111, 518, 1789, 5026, 12166, 26328, ...
0, 1, 22, 223, 1344, 5727, 19193, 54046, 133476, ...
|
|
|
MAPLE
|
with(numtheory):
A:= proc(n, k) option remember; `if`(n<2, 1, `if`(k=0, 0, add(
add(A(d, k-1)*d, d=divisors(j))*A(n-j, k), j=1..n)/n))
end:
seq(seq(A(n, d-n), n=0..d), d=0..14);
|
|
|
MATHEMATICA
|
A[n_, k_]:=b[n, k]=If[n<2, 1, If[k==0, 0, Sum[Sum[A[d, k - 1]*d, {d, Divisors[j]}] A[n - j, k], {j, n}]/n]]; Table[A[n, d - n], {d, 0, 14}, {n, 0, d}]//Flatten (* Indranil Ghosh, Jul 30 2017, after Maple code *)
|
|
|
CROSSREFS
|
Rows 0+1,2-10 give: A000012, A001477, A000217, A000330, A007715, A290360, A290361, A290362, A290363, A290364.
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A050338
|
|
Number of ways of factoring n with 2 levels of parentheses.
|
|
+10
10
|
|
|
|
1, 1, 1, 4, 1, 4, 1, 10, 4, 4, 1, 16, 1, 4, 4, 30, 1, 16, 1, 16, 4, 4, 1, 54, 4, 4, 10, 16, 1, 22, 1, 75, 4, 4, 4, 74, 1, 4, 4, 54, 1, 22, 1, 16, 16, 4, 1, 176, 4, 16, 4, 16, 1, 54, 4, 54, 4, 4, 1, 102, 1, 4, 16, 206, 4, 22, 1, 16, 4, 22, 1, 267, 1, 4, 16, 16, 4, 22, 1, 176, 30, 4, 1, 102
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
|
|
|
LINKS
|
|
|
|
FORMULA
|
Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A050336(n)).
|
|
|
EXAMPLE
|
4 = ((4)) = ((2*2)) = ((2)*(2)) = ((2))*((2)).
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A330459
|
|
Number of set partitions of set-systems with total sum n.
|
|
+10
10
|
|
|
|
1, 1, 1, 4, 6, 11, 26, 42, 78, 148, 280, 481, 867, 1569, 2742, 4933, 8493, 14857, 25925, 44877, 77022, 132511, 226449, 385396, 657314, 1111115, 1875708, 3157379, 5309439, 8885889, 14861478, 24760339, 41162971, 68328959, 113099231, 186926116, 308230044
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
Number of sets of disjoint nonempty sets of nonempty sets of positive integers with total sum n.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
The a(6) = 26 partitions:
((6)) ((15)) ((123)) ((1)(2)(12))
((24)) ((1)(14)) ((1))((2)(12))
((1)(5)) ((1)(23)) ((12))((1)(2))
((2)(4)) ((2)(13)) ((2))((1)(12))
((1))((5)) ((3)(12)) ((1))((2))((12))
((2))((4)) ((1))((14))
((1))((23))
((1)(2)(3))
((2))((13))
((3))((12))
((1))((2)(3))
((2))((1)(3))
((3))((1)(2))
((1))((2))((3))
|
|
|
MATHEMATICA
|
ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];
Table[Length[Select[ppl[n, 3], And[UnsameQ@@Join@@#, And@@UnsameQ@@@Join@@#]&]], {n, 0, 10}]
|
|
|
PROG
|
L(n)={eta(x^2 + O(x*x^n))/eta(x + O(x*x^n))}
BellP(n)={serlaplace(exp( exp(x + O(x*x^n)) - 1))}
seq(n)={my(c=L(n), b=BellP(n), v=Vec(prod(k=1, n, (1 + x^k*y + O(x*x^n))^polcoef(c, k)))); vector(#v, n, my(r=v[n]); sum(k=0, n-1, polcoeff(b, k)*polcoef(r, k)))} \\ Andrew Howroyd, Dec 29 2019
|
|
|
CROSSREFS
|
Cf. A007713, A050342, A050343, A279375, A279785, A283877, A294617, A330460, A330462, A323787-A323795, A330452-A330459.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A330452
|
|
Number of set partitions of strict multiset partitions of integer partitions of n.
|
|
+10
8
|
|
|
|
1, 1, 2, 7, 13, 34, 81, 175, 403, 890, 1977, 4262, 9356, 19963, 42573, 90865, 191206, 401803, 837898, 1744231, 3607504, 7436628, 15254309, 31185686, 63552725, 128963236, 260933000, 526140540, 1057927323, 2120500885, 4239012067, 8449746787, 16799938614
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Number of sets of disjoint nonempty sets of nonempty multisets of positive integers with total sum n.
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
The a(4) = 13 partitions:
((4)) ((22)) ((31)) ((211)) ((1111))
((1)(3)) ((1)(21)) ((1)(111))
((1))((3)) ((2)(11)) ((1))((111))
((1))((21))
((2))((11))
|
|
|
MATHEMATICA
|
ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];
Table[Length[Select[ppl[n, 3], UnsameQ@@Join@@#&]], {n, 0, 10}]
|
|
|
PROG
|
(PARI) \\ here BellP is A000110 as series.
BellP(n)={serlaplace(exp( exp(x + O(x*x^n)) - 1))}
seq(n)={my(b=BellP(n), v=Vec(prod(k=1, n, (1 + x^k*y + O(x*x^n))^numbpart(k)))); vector(#v, n, my(r=v[n]); sum(k=0, n-1, polcoeff(b, k)*polcoef(r, k)))} \\ Andrew Howroyd, Dec 29 2019
|
|
|
CROSSREFS
|
Cf. A001970, A007713, A050343, A063834, A089259, A261049, A271619, A279375, A294617, A318565, A323787-A323795, A330452-A330459, A330460.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A330461
|
|
Array read by antidiagonals where A(n,k) is the number of multiset partitions with k levels that are strict at all levels and have total sum n.
|
|
+10
5
|
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 4, 4, 1, 1, 1, 1, 4, 7, 7, 5, 1, 1, 1, 1, 5, 12, 14, 11, 6, 1, 1, 1, 1, 6, 19, 29, 25, 16, 7, 1, 1, 1, 1, 8, 30, 57, 60, 41, 22, 8, 1, 1, 1, 1, 10, 49, 110, 141, 111, 63, 29, 9, 1, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,12
|
|
|
LINKS
|
|
|
|
FORMULA
|
Column k is the k-th weigh transform of the all-ones sequence. The weigh transform of a sequence b has generating function Product_{i > 0} (1 + x^i)^b(i).
|
|
|
EXAMPLE
|
Array begins:
k=0 k=1 k=2 k=3 k=4 k=5 k=6
-----------------------------
n=0: 1 1 1 1 1 1 1
n=1: 1 1 1 1 1 1 1
n=2: 1 1 1 1 1 1 1
n=3: 1 2 3 4 5 6 7
n=4: 1 2 4 7 11 16 22
n=5: 1 3 7 14 25 41 63
n=6: 1 4 12 29 60 111 189
For example, the A(5,3) = 14 partitions are:
{{5}} {{1}}{{4}}
{{14}} {{2}}{{3}}
{{23}} {{1}}{{13}}
{{1}{4}} {{2}}{{12}}
{{2}{3}} {{1}}{{1}{3}}
{{1}{13}} {{2}}{{1}{2}}
{{2}{12}} {{1}}{{1}{12}}
|
|
|
MATHEMATICA
|
spl[n_, 0]:={n};
spl[n_, k_]:=Select[Join@@Table[Union[Sort/@Tuples[spl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}], UnsameQ@@#&];
Table[Length[spl[n-k, k]], {n, 0, 10}, {k, 0, n}]
|
|
|
PROG
|
(PARI)
WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
M(n, k=n)={my(L=List(), v=vector(n, i, 1)); listput(L, concat([1], v)); for(j=1, k, v=WeighT(v); listput(L, concat([1], v))); Mat(Col(L))~}
{ my(A=M(7)); for(i=1, #A, print(A[i, ])) } \\ Andrew Howroyd, Dec 31 2019
|
|
|
CROSSREFS
|
Cf. A001970, A004111, A007713, A060016, A273873, A279375, A279785, A294617, A306186, A323718, A323790, A330462.
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A055885
|
|
Euler transform applied twice to partition triangle A008284.
|
|
+10
4
|
|
|
|
1, 1, 3, 1, 3, 6, 1, 6, 9, 14, 1, 6, 18, 23, 27, 1, 9, 27, 54, 57, 58, 1, 9, 39, 87, 140, 131, 111, 1, 12, 51, 150, 259, 353, 295, 223, 1, 12, 69, 210, 470, 702, 832, 637, 424, 1, 15, 84, 314, 749, 1379, 1803, 1917, 1350, 817, 1, 15, 105, 416, 1176, 2352, 3730, 4403, 4245, 2789, 1527
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
1;
1, 3;
1, 3, 6;
1, 6, 9, 14;
1, 6, 18, 23, 27;
...
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A055886
|
|
Euler transform applied three times to partition triangle A008284.
|
|
+10
4
|
|
|
|
1, 1, 4, 1, 4, 10, 1, 8, 16, 30, 1, 8, 32, 54, 75, 1, 12, 48, 128, 176, 206, 1, 12, 70, 210, 443, 535, 518, 1, 16, 92, 362, 842, 1485, 1585, 1344, 1, 16, 124, 516, 1544, 3075, 4676, 4527, 3357, 1, 20, 152, 770, 2500, 6133, 10622, 14336, 12664, 8429, 1, 20, 190, 1030, 3952, 10718, 22524, 34918, 42426, 34631, 20759
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
1;
1, 4;
1, 4, 10;
1, 8, 16, 30;
1, 8, 32, 54, 75;
...
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A330472
|
|
Triangle read by rows where T(n,k) is the number of non-isomorphic k-element multisets of nonempty multisets of nonempty multisets (all finite).
|
|
+10
3
|
|
|
|
1, 0, 1, 0, 4, 2, 0, 10, 8, 3, 0, 33, 48, 18, 5, 0, 91, 204, 118, 32, 7, 0, 298, 959, 743, 266, 58, 11, 0, 910, 4193, 4334, 1927, 519, 94, 15, 0, 3017, 18947, 25305, 13992, 4407, 966, 154, 22, 0, 9945, 84798, 145033, 97947, 36410, 9023, 1679, 236, 30
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Triangle begins:
1
0 1
0 4 2
0 10 8 3
0 33 48 18 5
0 91 204 118 32 7
0 298 959 743 266 58 11
For example, row n = 3 counts the following multiset partitions:
{{111}} {{1}}{{11}} {{1}}{{1}}{{1}}
{{112}} {{1}}{{12}} {{1}}{{1}}{{2}}
{{123}} {{1}}{{23}} {{1}}{{2}}{{3}}
{{1}{11}} {{2}}{{11}}
{{1}{12}} {{1}}{{1}{1}}
{{1}{23}} {{1}}{{1}{2}}
{{2}{11}} {{1}}{{2}{3}}
{{1}{1}{1}} {{2}}{{1}{1}}
{{1}{1}{2}}
{{1}{2}{3}}
|
|
|
PROG
|
(PARI) \\ See links in A339645 for combinatorial species functions.
ColGf(k, n)={my(A=symGroupSeries(n)); OgfSeries(sCartProd(sExp(A), sSubstOp(polcoef(A, k, x)*x^k + O(x*x^n), sExp(A)) ))}
M(n, m=n)={Mat(vector(m+1, k, Col(ColGf(k-1, n), -(n+1))))}
{ my(A=M(10)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Jan 17 2023
|
|
|
CROSSREFS
|
Column k = 1 is A007716 (for n > 0).
Partitions of partitions of partitions are A007713.
If this is the 3-dimensional version, the 2-dimensional version is A317533.
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A330473
|
|
Regular triangle where T(n,k) is the number of non-isomorphic multiset partitions of k-element multiset partitions of multisets of size n.
|
|
+10
2
|
|
|
|
1, 0, 1, 0, 2, 4, 0, 3, 8, 10, 0, 5, 28, 38, 33, 0, 7, 56, 146, 152, 91, 0, 11, 138, 474, 786, 628, 298, 0, 15, 268, 1388, 3117, 3808, 2486, 910, 0, 22, 570, 3843, 11830, 19147, 18395, 9986, 3017, 0, 30, 1072, 10094, 40438, 87081, 110164, 86388, 39889, 9945
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
COMMENTS
|
As an alternative description, T(n,k) is the number of non-isomorphic multisets of nonempty multisets of nonempty multisets with n leaves whose multiset union consists of k multisets.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Triangle begins:
1
0 1
0 2 4
0 3 8 10
0 5 28 38 33
0 7 56 146 152 91
0 11 138 474 786 628 298
For example, row n = 3 counts the following multiset partitions:
{{111}} {{1}{11}} {{1}{1}{1}}
{{112}} {{1}{12}} {{1}{1}{2}}
{{123}} {{1}{23}} {{1}{2}{3}}
{{2}{11}} {{1}}{{1}{1}}
{{1}}{{11}} {{1}}{{1}{2}}
{{1}}{{12}} {{1}}{{2}{3}}
{{1}}{{23}} {{2}}{{1}{1}}
{{2}}{{11}} {{1}}{{1}}{{1}}
{{1}}{{1}}{{2}}
{{1}}{{2}}{{3}}
|
|
|
PROG
|
(PARI) \\ See links in A339645 for combinatorial species functions.
ColGf(k, n)={my(A=symGroupSeries(n)); OgfSeries(sCartProd(sExp(A), sSubstOp(polcoef(sExp(A), k, x)*x^k + O(x*x^n), A) ))}
M(n, m=n)={Mat(vector(m+1, k, Col(ColGf(k-1, n), -(n+1))))}
{ my(A=M(10)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Jan 18 2023
|
|
|
CROSSREFS
|
Column k = 1 is A000041 (for n > 0).
Partitions of partitions of partitions are A007713.
The 2-dimensional version is A317533.
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.011 seconds
|
