A341796 Number of ways to write n as an ordered sum of 5 nonzero tetrahedral numbers.

1, 0, 0, 5, 0, 0, 10, 0, 0, 15, 0, 0, 25, 0, 0, 31, 0, 0, 30, 5, 0, 35, 20, 0, 30, 30, 0, 20, 40, 0, 20, 65, 0, 10, 65, 0, 5, 70, 10, 5, 90, 30, 0, 70, 30, 1, 85, 40, 0, 80, 60, 0, 50, 50, 0, 70, 90, 10, 50, 90, 20, 50, 80, 10, 60, 130, 20, 65, 70, 20, 65, 90, 30, 50, 110, 70, 65, 100

Offset: 5

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 5..1000

Crossrefs

Cf. A000292, A023533, A023670, A282172, A282582, A340950, A341776, A341794, A341795, A341797, A341806, A341807, A341808, A341809.

Programs

Magma

R:=PowerSeriesRing(Integers(), 100);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^5 )); // G. C. Greubel, Jul 20 2022

Mathematica

nmax = 82; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

SageMath

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
def A341796_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(5, x) ).list()
a=A341796_list(120); a[5:100] # G. C. Greubel, Jul 20 2022

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^5.