|
| |
|
|
A225029
|
|
Non-crossing, non-nesting, 3-colored set partitions.
|
|
2
|
|
|
|
1, 4, 19, 103, 616, 3949, 26545, 184120, 1303135, 9341191, 67490044, 489978217, 3567727441, 26024391436, 190036459099, 1388593185079, 10150390743088, 74215146065461, 542704850311009, 3968914608295360, 29026988765886535, 212297824609934455, 1552734183515322436
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: (1 - 10*x + 22*x^2 - x^3)/(1 - 14*x + 59*x^2 - 74*x^3 + x^4).
a(n) = 14*a(n-1) -59*a(n-2) +74*a(n-3) -a(n-4), with a(0) = 1, a(1) = 4, a(2) = 19 and a(3) = 103. - Muniru A Asiru, Dec 18 2018
|
|
|
EXAMPLE
|
a(3) = 103 is the number of non-crossing, non-nesting, 3-colored set partitions on {1,2,3,4}.
|
|
|
MAPLE
|
seq(coeff(series((1-10*x+22*x^2-x^3)/(1-14*x+59*x^2-74*x^3+x^4), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Dec 18 2018
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1 - 10 x + 22 x^2 - x^3) / (1 - 14 x + 59 x^2 - 74 x^3 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 20 2018 *)
|
|
|
PROG
|
(PARI) Vec((1-10*x+22*x^2-x^3)/(1-14*x+59*x^2-74*x^3+x^4)+O(x^66)) \\ Joerg Arndt, Apr 24 2013
(GAP) a:=[1, 4, 19, 103];; for n in [5..25] do a[n]:=14*a[n-1]-59*a[n-2]+74*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Dec 18 2018
(Magma) I:=[1, 4, 19, 103]; [n le 4 select I[n] else 14*Self(n-1)-59*Self(n-2)+74*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 20 2018
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
