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A241550 Number of partitions p of n such that (number of numbers of the form 5k + 1 in p) is a part of p. 5
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

Cf. A241549, A241551, A241552, A241553.

Sequence in context: A107332 A002062 A005688 * A319564 A221943 A120446

Adjacent sequences:  A241547 A241548 A241549 * A241551 A241552 A241553

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 26 2014

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)