A238482 - OEIS

A238482

Number of partitions p of n containing floor((min(p) + max(p))/2) as a part.

1, 2, 3, 4, 5, 7, 9, 11, 16, 20, 25, 35, 45, 54, 76, 95, 117, 154, 196, 239, 309, 384, 471, 595, 737, 893, 1116, 1364, 1653, 2032, 2470, 2974, 3618, 4363, 5235, 6309, 7563, 9014, 10796, 12863, 15264, 18157, 21517, 25416, 30069, 35455, 41710, 49084, 57629

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..49.

FORMULA

a(n) + A238483(n) = A000041(n).

EXAMPLE

a(6) counts these partitions: 6, 33, 221, 222, 2211, 21111, 111111.

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Floor[(Min[p] + Max[p])/2]]], {n, 50}]

CROSSREFS