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A241069

Number of partitions p of n into distinct parts such that max(p) = 4*min(p).

0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 3, 4, 3, 3, 3, 4, 6, 6, 4, 6, 5, 8, 8, 9, 9, 10, 13, 11, 13, 15, 17, 20, 21, 21, 24, 25, 29, 30, 33, 35, 40, 44, 44, 49, 51, 56, 61, 66, 69, 77, 82, 91, 95, 102, 106, 116, 127, 134, 147, 157, 168, 182

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OFFSET

0,11

LINKS

Table of n, a(n) for n=0..70.

FORMULA

G.f.: Sum_{j>=1} q^(5*j) * Product_{k=j+1..4*j-1} (1+q^k). - Seiichi Manyama, Mar 05 2026

EXAMPLE

a(10) counts these 2 partitions: 82, 4321.

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 *)