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A281083 Expansion of Product_{k>=0} (1 + x^(5*k*(k+1)/2+1)). 6
1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,83

COMMENTS

Number of partitions of n into distinct centered pentagonal numbers (A005891).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1001 terms from G. C. Greubel)

Eric Weisstein's World of Mathematics, Centered Pentagonal 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^(5*k*(k+1)/2+1)).

EXAMPLE

a(82) = 2 because we have [76, 6] and [51, 31].

MATHEMATICA

nmax = 105; CoefficientList[Series[Product[1 + x^(5 k (k + 1)/2 + 1), {k, 0, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A005891, A218380, A280952, A281081, A281082, A281084.

Sequence in context: A186230 A214304 A248640 * A230629 A027359 A236109

Adjacent sequences:  A281080 A281081 A281082 * A281084 A281085 A281086

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 14 2017

STATUS

approved

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Last modified May 23 14:00 EDT 2022. Contains 353975 sequences. (Running on oeis4.)