A279281 Expansion of Product_{k>=1} (1 + x^(k*(3*k-2))).

1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1

Offset

0,106

Comments

Number of partitions of n into distinct octagonal numbers (A000567).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 + x^(k*(3*k-2))).

Example

a(105) = 2 because we have [96, 8, 1] and [65, 40].

Mathematica

nmax = 120; CoefficientList[Series[Product[1 + x^(k (3 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000567, A024940, A033461, A218380, A279041, A279279, A279280.

Sequence in context: A368844 A181563 A056976 * A342465 A124749 A350890

Adjacent sequences: A279278 A279279 A279280 * A279282 A279283 A279284

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 09 2016

Status

approved