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A341797
Number of ways to write n as an ordered sum of 6 nonzero tetrahedral numbers.
8
1, 0, 0, 6, 0, 0, 15, 0, 0, 26, 0, 0, 45, 0, 0, 66, 0, 0, 76, 6, 0, 90, 30, 0, 96, 60, 0, 80, 90, 0, 75, 150, 0, 60, 192, 0, 35, 210, 15, 30, 270, 60, 15, 270, 90, 6, 270, 120, 6, 306, 195, 0, 240, 210, 1, 246, 270, 20, 240, 360, 60, 180, 330, 60, 216, 450, 80, 210, 435, 120, 216, 360
OFFSET
6,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^6.
MATHEMATICA
nmax = 77; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^6 )); // G. C. Greubel, Jul 20 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..20) ) )^m
def A341797_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(6, x) ).list()
a=A341797_list(100); a[6:81] # G. C. Greubel, Jul 20 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 19 2021
STATUS
approved