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A281084 Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)+1)). 5
1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,99

COMMENTS

Number of partitions of n into distinct centered hexagonal numbers (A003215).

LINKS

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

Eric Weisstein's World of Mathematics, Hex Number

Index entries for sequences related to centered polygonal numbers

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)+1)).

EXAMPLE

a(98) = 2 because we have [91, 7] and [61, 37].

MATHEMATICA

nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1) + 1), {k, 0, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A003215, A279279, A280953, A281081, A281082, A281083.

Sequence in context: A300717 A191928 A033148 * A186230 A214304 A248640

Adjacent sequences:  A281081 A281082 A281083 * A281085 A281086 A281087

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 14 2017

STATUS

approved

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Last modified July 7 12:47 EDT 2022. Contains 355148 sequences. (Running on oeis4.)