login
A341808
Number of ways to write n as an ordered sum of 9 nonzero tetrahedral numbers.
6
1, 0, 0, 9, 0, 0, 36, 0, 0, 93, 0, 0, 198, 0, 0, 378, 0, 0, 624, 9, 0, 918, 72, 0, 1269, 252, 0, 1597, 576, 0, 1836, 1134, 0, 2025, 2025, 0, 2058, 3096, 36, 1926, 4356, 252, 1764, 5877, 756, 1470, 7182, 1512, 1134, 8388, 2772, 882, 9576, 4608, 588, 10035, 6552, 462
OFFSET
9,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^9.
MATHEMATICA
nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 70);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..70]])^9 )); // G. C. Greubel, Jul 18 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..8) ) )^m
def A341808_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(9, x) ).list()
a=A341808_list(100); a[9:71] # G. C. Greubel, Jul 18 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 20 2021
STATUS
approved