A241550 - OEIS

A241550

Number of partitions p of n such that (number of numbers of the form 5k + 1 in p) is a part of p.

0, 1, 1, 2, 3, 5, 7, 10, 14, 21, 28, 39, 51, 70, 92, 122, 158, 206, 265, 343, 432, 554, 695, 879, 1098, 1373, 1703, 2115, 2607, 3218, 3937, 4831, 5882, 7175, 8699, 10541, 12733, 15358, 18464, 22184, 26548, 31774, 37891, 45166, 53681, 63743, 75529, 89381

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OFFSET

0,4

COMMENTS

Each number in p is counted once, regardless of its multiplicity.

LINKS

Table of n, a(n) for n=0..47.

EXAMPLE

a(6) counts these 7 partitions: 51, 411, 321, 3111, 2211, 21111, 111111.

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*)