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A241063

Number of partitions p of n into distinct parts such that max(p) = 3*min(p).

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 3, 2, 1, 1, 3, 2, 2, 3, 4, 3, 3, 5, 4, 5, 5, 7, 7, 7, 7, 7, 9, 10, 10, 11, 13, 14, 14, 14, 15, 17, 19, 22, 24, 23, 24, 28, 28, 31, 32, 36, 39, 42, 43, 46, 49, 53, 56, 59, 65, 68, 73, 77, 81, 87, 92

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OFFSET

0,13

LINKS

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

FORMULA

G.f.: Sum_{j>=1} q^(4*j) * Product_{k=j+1..3*j-1} (1+q^k). - Seiichi Manyama, Mar 05 2026

EXAMPLE

a(12) counts these 2 partitions: 93, 642.

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 *)

Table[Count[f[n], p_ /; Max[p] == 5*Min[p]], {n, 0, z}] (* A241272 *)

Table[Count[f[n], p_ /; Max[p] == 6*Min[p]], {n, 0, z}] (* A241273 *)

CROSSREFS

Cf. A241035, A241069, A241272, A241273.

Sequence in context: A267109 A341524 A175804 * A340251 A286957 A195017

Adjacent sequences: A241060 A241061 A241062 * A241064 A241065 A241066

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 18 2014

STATUS

approved

URL: https://oeis.org/A241063

⇱ A241063 - OEIS