A341794 Number of ways to write n as an ordered sum of 3 nonzero tetrahedral numbers.

1, 0, 0, 3, 0, 0, 3, 0, 0, 4, 0, 0, 6, 0, 0, 3, 0, 0, 3, 3, 0, 3, 6, 0, 0, 3, 0, 1, 6, 0, 0, 6, 0, 0, 3, 0, 0, 9, 3, 0, 3, 3, 0, 6, 0, 0, 6, 3, 0, 0, 0, 0, 3, 6, 0, 3, 6, 1, 6, 0, 0, 3, 6, 0, 6, 0, 0, 6, 3, 0, 0, 3, 3, 3, 6, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 6, 3, 0, 9, 0, 0, 12

Offset: 3

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

• nonn

Crossrefs

Cf. A000292, A023533, A023670, A053604, A282582, A341774, A341795, A341796, A341797.

Programs

Mathematica

nmax = 95; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^3, {x, 0, nmax}], x] // Drop[#, 3] &

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^3.