A241553 Number of partitions p of n such that (number of numbers of the form 5k + 4 in p) is a part of p.

0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 25, 33, 49, 65, 90, 119, 159, 210, 277, 358, 466, 593, 766, 968, 1231, 1548, 1942, 2427, 3026, 3747, 4642, 5704, 7022, 8587, 10498, 12775, 15519, 18799, 22730, 27394, 32981, 39558, 47426, 56676, 67650, 80564, 95781

Offset

0,8

Comments

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

Links

Table of n, a(n) for n=0..49.

Example

a(6) counts this single partition:  411.

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, A241552.

Sequence in context: A240202 A235945 A129504 * A241549 A266773 A347448

Adjacent sequences: A241550 A241551 A241552 * A241554 A241555 A241556

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved