A241551 Number of partitions p of n such that (number of numbers of the form 5k + 2 in p) is a part of p.

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.

Links

Table of n, a(n) for n=0..48.

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

Cf. A241549, A241550, A241552, A241553.

Sequence in context: A121367 A308495 A221672 * A070217 A256121 A308869

Adjacent sequences: A241548 A241549 A241550 * A241552 A241553 A241554

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved