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

Author

Ilya Gutkovskiy, Aug 14 2017

Keywords

• nonn

Examples

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

Links

• Eric Weisstein's World of Mathematics, Pentagonal Number
• Index to sequences related to polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

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

Programs

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]

Formula

G.f.: Product_{k>=1} (1 + x^(k*(3*k-1)/2))*(1 + x^(k*(3*k+1)/2)).