A294624 Number of partitions of n into distinct generalized octagonal numbers (A001082).

1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 2, 0, 0, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 1, 0, 2, 3, 1, 1, 2, 2, 1, 0, 1, 3, 2, 2, 3, 1, 1, 1, 3, 5, 2, 2, 3, 2, 2, 1, 3, 5, 2, 1, 3, 3, 2, 1, 3, 6, 3, 1, 3, 4, 3, 1, 4, 7, 3, 0, 3, 6, 4, 1, 2, 7, 5, 2, 4, 5, 5, 2

Offset: 0

Author

Ilya Gutkovskiy, Nov 05 2017

Keywords

• nonn

Examples

			a(21) = 2 because we have [21] and [16, 5].
		

Links

• Eric Weisstein's World of Mathematics, Octagonal Number
• Index to sequences related to polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A001082, A024940, A279281, A290942, A294622, A294623.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^(k (3 k - 2))) (1 + x^(k (3 k + 2))), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

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