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

0,36

Comments

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

Links

Table of n, a(n) for n=0..120.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000292, A007294, A024940, A068980.

Sequence in context: A363339 A334195 A348446 * A015964 A088950 A267113

Adjacent sequences: A279275 A279276 A279277 * A279279 A279280 A279281

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 09 2016

Status

approved