A341797 Number of ways to write n as an ordered sum of 6 nonzero tetrahedral numbers.

1, 0, 0, 6, 0, 0, 15, 0, 0, 26, 0, 0, 45, 0, 0, 66, 0, 0, 76, 6, 0, 90, 30, 0, 96, 60, 0, 80, 90, 0, 75, 150, 0, 60, 192, 0, 35, 210, 15, 30, 270, 60, 15, 270, 90, 6, 270, 120, 6, 306, 195, 0, 240, 210, 1, 246, 270, 20, 240, 360, 60, 180, 330, 60, 216, 450, 80, 210, 435, 120, 216, 360

Offset

6,4

Links

G. C. Greubel, Table of n, a(n) for n = 6..1000

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^6.

Mathematica

nmax = 77; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^6 )); // 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 A341797_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(6, x) ).list()
a=A341797_list(100); a[6:81] # G. C. Greubel, Jul 20 2022

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340951, A341777, A341794, A341795, A341796, A341797, A341806, A341807, A341808, A341809.

Sequence in context: A028592 A243254 A263850 * A340905 A210446 A002044

Adjacent sequences: A341794 A341795 A341796 * A341798 A341799 A341800

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2021

Status

approved