A341809 Number of ways to write n as an ordered sum of 10 nonzero tetrahedral numbers.

1, 0, 0, 10, 0, 0, 45, 0, 0, 130, 0, 0, 300, 0, 0, 612, 0, 0, 1095, 10, 0, 1740, 90, 0, 2565, 360, 0, 3490, 930, 0, 4351, 1980, 0, 5130, 3790, 0, 5680, 6330, 45, 5820, 9540, 360, 5715, 13620, 1260, 5292, 17950, 2880, 4530, 22140, 5670, 3780, 26490, 10170, 2940, 29770, 15840

Offset

10,4

Links

G. C. Greubel, Table of n, a(n) for n = 10..1000

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^10.

Mathematica

nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 70);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..70]])^10 )); // G. C. Greubel, Jul 18 2022
(Sage)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..8) ) )^m
def A341809_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( f(10, x) ).list()
a=A341809_list(100); a[10:71]  # G. C. Greubel, Jul 18 2022

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340955, A341793, A341794, A341795, A341796, A341797, A341806, A341807, A341808.

Sequence in context: A288435 A287734 A064511 * A340947 A306934 A003785

Adjacent sequences: A341806 A341807 A341808 * A341810 A341811 A341812

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 20 2021

Status

approved