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

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 A347869 A221943

Adjacent sequences: A241547 A241548 A241549 * A241551 A241552 A241553

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved