A239946 - OEIS

A239946

Number of partitions of n not containing the number of distinct parts as a part.

1, 0, 1, 1, 3, 3, 6, 8, 12, 16, 23, 32, 42, 58, 74, 102, 131, 170, 220, 283, 359, 462, 579, 727, 922, 1136, 1424, 1763, 2183, 2667, 3308, 4019, 4917, 5982, 7285, 8774, 10666, 12797, 15437, 18505, 22181, 26481, 31678, 37649, 44773, 53177, 62994, 74466, 88014

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..48.

FORMULA

a(n) + A239945(n) = A000041(n) for n >= 0.

EXAMPLE

a(7) counts these 8 partitions: 7, 61, 511, 43, 421, 4111, 331, 31111.

MATHEMATICA

z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, d[p]]], {n, 0, z}] (* A239945 *)

Table[PartitionsP[n] - t[[n + 1]], {n, 0, z}] (* A239946 *)