A281083 Expansion of Product_{k>=0} (1 + x^(5*k*(k+1)/2+1)).

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

Offset: 0

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

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

Programs

Mathematica

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

Formula

G.f.: Product_{k>=0} (1 + x^(5*k*(k+1)/2+1)).