A281081 Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).

1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 3, 1, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 3, 1, 0, 0, 1, 2

Offset: 0

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn

Comments

Number of partitions of n into distinct centered triangular numbers (A005448).

Examples

			a(46) = 2 because we have [46] and [31, 10, 4, 1].
		

Links

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

Crossrefs

Cf. A005448, A024940, A279278, A280950, A281082, A281083, A281084.

Programs

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1)/2 + 1), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).