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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
OFFSET
0,8
COMMENTS
Each number in p is counted once, regardless of its multiplicity.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 26 2014
STATUS
approved