A241552 Number of partitions p of n such that (number of numbers of the form 5k + 3 in p) is a part of p.

0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 23, 34, 47, 64, 87, 115, 154, 204, 266, 346, 444, 573, 731, 933, 1174, 1479, 1855, 2320, 2884, 3578, 4411, 5443, 6678, 8185, 9977, 12157, 14753, 17886, 21608, 26058, 31326, 37631, 45066, 53911, 64300, 76609, 91061

Offset

0,7

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 2 partitions:  321, 3111.

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, A241551, A241553.

Sequence in context: A177205 A275580 A175829 * A175827 A061535 A280276

Adjacent sequences: A241549 A241550 A241551 * A241553 A241554 A241555

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved