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

Author

Clark Kimberling, Apr 26 2014

Keywords

• nonn
• easy

Comments

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

Examples

			a(6) counts this single partition:  411.
		

Crossrefs

Cf. A241549, A241550, A241551, A241552.

Programs

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 *)