A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.

1, 0, 0, 7, 0, 0, 21, 0, 0, 42, 0, 0, 77, 0, 0, 126, 0, 0, 168, 7, 0, 211, 42, 0, 252, 105, 0, 252, 182, 0, 245, 315, 0, 231, 469, 0, 175, 574, 21, 140, 735, 105, 105, 854, 210, 56, 875, 315, 42, 987, 525, 21, 952, 693, 7, 882, 840, 42, 924, 1155, 140, 770, 1260, 211, 749, 1470

Offset: 7

Author

Ilya Gutkovskiy, Feb 20 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 7..1000

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340952, A341778, A341794, A341795, A341796, A341797, A341807, A341808, A341809.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^7 )); // G. C. Greubel, Jul 19 2022

Mathematica

nmax = 72; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

SageMath

def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
def A341806_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(7, x) ).list()
a=A341806_list(100); a[7:81] # G. C. Greubel, Jul 19 2022

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^7.