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A241272

Number of partitions p of n into distinct parts such that max(p) = 5*min(p).

0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 2, 2, 2, 3, 3, 4, 6, 5, 5, 7, 7, 9, 11, 10, 11, 12, 12, 14, 18, 18, 18, 21, 21, 24, 27, 30, 30, 36, 37, 42, 47, 49, 54, 60, 64, 71, 81, 83, 91, 100, 107, 116, 129, 136, 147, 159, 172, 184, 200, 213, 228

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OFFSET

0,13

LINKS

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

FORMULA

G.f.: Sum_{j>=1} q^(6*j) * Product_{k=j+1..5*j-1} (1+q^k). - Seiichi Manyama, Mar 05 2026

EXAMPLE

a(12) counts these 2 partitions: {10,2}, {5,4,2,1}.

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 *)