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

3,4

Links

Table of n, a(n) for n=3..95.

Formula

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

Example

a(3)=1 counts the composition 3=1+1+1. a(6)=3 counts the 3 compositions 6 = 1+1+4 = 1+4+1 = 4+1+1.

Mathematica

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

Crossrefs

Cf. A000292, A023533, A023670, A053604, A282582, A341774 (partitions instead compositions), A341795, A341796, A341797.

Sequence in context: A361824 A293903 A284444 * A033685 A272974 A063691

Adjacent sequences: A341791 A341792 A341793 * A341795 A341796 A341797

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2021

Status

approved