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

5,4

Links

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

Formula

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

Mathematica

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

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 100);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^5 )); // G. C. Greubel, Jul 20 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..20) ) )^m
def A341796_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(5, x) ).list()
a=A341796_list(120); a[5:100] # G. C. Greubel, Jul 20 2022

Crossrefs

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

Sequence in context: A256929 A068459 A099222 * A340481 A236232 A019178

Adjacent sequences: A341793 A341794 A341795 * A341797 A341798 A341799

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2021

Status

approved