A279278 Expansion of Product_{k>=1} (1 + x^(k*(k+1)*(k+2)/6)).

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

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn

Comments

Number of partitions of n into distinct tetrahedral numbers (A000292).

Examples

			a(35) = 2 because we have [35] and [20, 10, 4, 1].
		

Links

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

Crossrefs

Cf. A000292, A007294, A024940, A068980, A350205 (positions of records).

Programs

Mathematica

nmax=120; CoefficientList[Series[Product[1 + x^(k (k + 1) (k + 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + x^(k*(k+1)*(k+2)/6)).