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A290942 Number of partitions of n into distinct generalized pentagonal numbers (A001318). 5
1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 4, 3, 3, 3, 2, 5, 4, 5, 4, 2, 3, 3, 6, 6, 5, 5, 4, 5, 7, 8, 8, 7, 6, 6, 6, 8, 9, 9, 9, 7, 8, 9, 9, 11, 10, 11, 11, 10, 12, 10, 14, 15, 14, 14, 11, 13, 13, 17, 17, 14, 15, 14, 17, 20, 19, 20, 20, 20, 21, 20, 21, 21, 25, 26, 23, 22, 21, 24, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..90.

Eric Weisstein's World of Mathematics, Pentagonal 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-1)/2))*(1 + x^(k*(3*k+1)/2)).

EXAMPLE

a(15) = 3 because we have [15], [12, 2, 1] and [7, 5, 2, 1].

MATHEMATICA

nmax = 90; CoefficientList[Series[Product[(1 + x^(k (3 k - 1)/2)) (1 + x^(k (3 k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000009, A001318, A095699, A218379, A218380, A279221, A280952, A281083.

Sequence in context: A241079 A061198 A195011 * A039801 A105821 A004564

Adjacent sequences:  A290939 A290940 A290941 * A290943 A290944 A290945

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 14 2017

STATUS

approved

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Last modified February 23 09:30 EST 2018. Contains 299508 sequences. (Running on oeis4.)