A341807 Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.

1, 0, 0, 8, 0, 0, 28, 0, 0, 64, 0, 0, 126, 0, 0, 224, 0, 0, 336, 8, 0, 456, 56, 0, 589, 168, 0, 672, 336, 0, 708, 616, 0, 728, 1016, 0, 658, 1400, 28, 560, 1856, 168, 476, 2352, 420, 336, 2632, 728, 238, 2968, 1260, 168, 3192, 1904, 84, 3096, 2464, 112, 3192, 3360, 308, 3024, 4144

Offset: 8

Author

Ilya Gutkovskiy, Feb 20 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 8..1000

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340953, A341791, A341794, A341795, A341796, A341797, A341806, A341808, A341809.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^8 )); // G. C. Greubel, Jul 19 2022

Mathematica

nmax = 70; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

SageMath

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
def A341807_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(8, x) ).list()
a=A341807_list(100); a[8:81] # G. C. Greubel, Jul 19 2022

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^8.