A241273 - OEIS

A241273

Number of partitions p of n into distinct parts such that max(p) = 6*min(p).

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 1, 2, 2, 2, 2, 1, 4, 2, 3, 3, 5, 5, 6, 8, 8, 9, 10, 13, 14, 16, 18, 20, 20, 24, 25, 28, 31, 36, 37, 40, 42, 46, 51, 55, 62, 65, 72, 76, 83, 89, 98, 107, 117, 126, 139, 149, 163, 177, 195, 208, 226, 247, 267, 291

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OFFSET

0,13

LINKS

Table of n, a(n) for n=0..68.

EXAMPLE

a(14) counts these 3 partitions: {12,2}, {6,5,2,1}, {6,4,3,1}.

MATHEMATICA

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)

Table[Count[f[n], p_ /; Max[p] == 3*Min[p]], {n, 0, z}] (* A241063 *)

Table[Count[f[n], p_ /; Max[p] == 4*Min[p]], {n, 0, z}] (* A241069 *)