login
A241547
Number of partitions p of n such that (number of numbers of the form 3k+1 in p) is a part of p.
3
0, 1, 1, 2, 3, 4, 6, 10, 12, 18, 25, 33, 45, 63, 77, 107, 139, 177, 231, 302, 372, 486, 612, 762, 969, 1214, 1489, 1879, 2315, 2839, 3522, 4318, 5243, 6460, 7835, 9483, 11558, 13938, 16763, 20285, 24302, 29087, 34941, 41642, 49588, 59198, 70199, 83205, 98780
OFFSET
0,4
COMMENTS
Each number in p is counted once, regardless of its multiplicity.
EXAMPLE
a(6) counts these 6 partitions: 51, 321, 3111, 2211, 21111, 111111.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241546 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241547 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241548 *)
CROSSREFS
Sequence in context: A288784 A322164 A237823 * A273542 A061018 A130126
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 26 2014
STATUS
approved