A241064 - OEIS

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A241064

Number of partitions p of n into distinct parts such that max(p) > 1 + 2*min(p).

0, 0, 0, 0, 0, 1, 1, 2, 4, 4, 6, 8, 11, 13, 16, 21, 26, 32, 38, 45, 56, 66, 79, 94, 110, 128, 151, 178, 207, 240, 277, 320, 370, 426, 488, 561, 642, 732, 834, 948, 1079, 1225, 1388, 1570, 1774, 2002, 2254, 2540, 2856, 3206, 3598, 4034, 4516, 5050, 5642, 6298

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) + A241061(n) + A241062(n) = A000009(n) for n >= 1.

a(n) = A241037(n) - A241062(n) for n>= 0.

EXAMPLE

a(10) counts these 6 partitions: 91, 82, 721, 631, 541, 4321

MATHEMATICA

z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];