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A240489
Number of partitions of n containing m(4) as a part, where m denotes multiplicity.
5
0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 7, 10, 14, 20, 27, 38, 52, 70, 93, 123, 161, 210, 272, 350, 447, 571, 722, 911, 1144, 1430, 1782, 2213, 2736, 3374, 4146, 5082, 6208, 7567, 9194, 11146, 13481, 16265, 19579, 23522, 28192, 33731, 40274, 47998, 57096, 67805, 80379
OFFSET
0,8
EXAMPLE
a(10) counts these 7 partitions: 541, 442, 4321, 43111, 42211, 421111, 4111111.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A240486 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2]]], {n, 0, z}] (* A240487 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 3]]], {n, 0, z}] (* A240488 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 4]]], {n, 0, z}] (* A240489 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 5]]], {n, 0, z}] (* A240490 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved