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

8,4

Links

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

Formula

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

Mathematica

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

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..70]])^8 )); // G. C. Greubel, Jul 19 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..8) ) )^m
def A341807_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(8, x) ).list()
a=A341807_list(100); a[8:81] # G. C. Greubel, Jul 19 2022

Crossrefs

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

Sequence in context: A028593 A369380 A037216 * A340915 A028701 A126270

Adjacent sequences: A341804 A341805 A341806 * A341808 A341809 A341810

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 20 2021

Status

approved