A290942 Number of partitions of n into distinct generalized pentagonal numbers (A001318).

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

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 A342936

Adjacent sequences: A290939 A290940 A290941 * A290943 A290944 A290945

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 14 2017

Status

approved