A294622 - OEIS

A294622

Number of partitions of n into generalized octagonal numbers (A001082).

1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 8, 8, 9, 9, 10, 13, 13, 14, 16, 17, 20, 20, 21, 24, 25, 28, 31, 33, 36, 37, 40, 45, 47, 50, 55, 59, 65, 67, 70, 77, 81, 87, 94, 99, 107, 111, 117, 127, 133, 141, 152, 160, 172, 178, 186, 201, 210, 223, 237, 249, 267, 276, 289, 308, 322, 341, 360, 378, 401

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..74.

Eric Weisstein's World of Mathematics, Octagonal Number

Index to sequences related to polygonal numbers

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/((1 - x^(k*(3*k-2)))*(1 - x^(k*(3*k+2)))).

EXAMPLE

a(8) = 3 because we have [8], [5, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].