|
| |
|
|
A336866
|
|
Number of integer partitions of n without all distinct multiplicities.
|
|
10
|
|
|
|
0, 0, 0, 1, 1, 2, 4, 5, 9, 15, 21, 28, 46, 56, 80, 114, 149, 192, 269, 337, 455, 584, 751, 943, 1234, 1527, 1944, 2422, 3042, 3739, 4699, 5722, 7100, 8668, 10634, 12880, 15790, 19012, 23093, 27776, 33528, 40102, 48264, 57469, 68793, 81727, 97372, 115227
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
The a(0) = 0 through a(9) = 15 partitions (empty columns shown as dots):
. . . (21) (31) (32) (42) (43) (53) (54)
(41) (51) (52) (62) (63)
(321) (61) (71) (72)
(2211) (421) (431) (81)
(3211) (521) (432)
(3221) (531)
(3311) (621)
(4211) (3321)
(32111) (4221)
(4311)
(5211)
(32211)
(42111)
(222111)
(321111)
|
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Length/@Split[#]&]], {n, 0, 30}]
|
|
|
CROSSREFS
|
A130092 gives the Heinz numbers of these partitions.
A001222 counts prime factors with multiplicity.
A013929 lists nonsquarefree numbers.
A047967 counts non-strict partitions.
A071625 counts distinct prime multiplicities.
A130091 lists numbers with distinct prime multiplicities.
A181796 counts divisors with distinct prime multiplicities.
A327498 gives the maximum divisor with distinct prime multiplicities.
Cf. A000009, A000041, A008284, A116608, A118914, A124010, A242882, A255231, A325280, A325242, A329739, A336422, A336571.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
