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

Author

Ilya Gutkovskiy, Feb 20 2021

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Magma

R:=PowerSeriesRing(Integers(), 70);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^10 )); // G. C. Greubel, Jul 18 2022

Mathematica

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

Sage

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
def A341809_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(10, x) ).list()
a=A341809_list(100); a[10:71]  # G. C. Greubel, Jul 18 2022

Formula

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