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A241553 Number of partitions p of n such that (number of numbers of the form 5k + 4 in p) is a part of p. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A024789

Adjacent sequences:  A241550 A241551 A241552 * A241554 A241555 A241556

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 26 2014

STATUS

approved

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Last modified July 12 21:31 EDT 2020. Contains 335669 sequences. (Running on oeis4.)