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A241551
Number of partitions p of n such that (number of numbers of the form 5k + 2 in p) is a part of p.
7
0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 16, 25, 34, 49, 66, 90, 119, 161, 211, 279, 357, 465, 595, 764, 968, 1224, 1536, 1933, 2406, 2999, 3703, 4577, 5628, 6910, 8441, 10295, 12507, 15184, 18356, 22163, 26661, 32035, 38395, 45937, 54821, 65321, 77655, 92209, 109242
OFFSET
0,6
COMMENTS
Each number in p is counted once, regardless of its multiplicity.
EXAMPLE
a(6) counts these 3 partitions: 321, 2211, 21111.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241549 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241550 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241551 *)
Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}] (* A241552 *)
Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}] (* A241553 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 26 2014
STATUS
approved