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A341796
Number of ways to write n as an ordered sum of 5 nonzero tetrahedral numbers.
8
1, 0, 0, 5, 0, 0, 10, 0, 0, 15, 0, 0, 25, 0, 0, 31, 0, 0, 30, 5, 0, 35, 20, 0, 30, 30, 0, 20, 40, 0, 20, 65, 0, 10, 65, 0, 5, 70, 10, 5, 90, 30, 0, 70, 30, 1, 85, 40, 0, 80, 60, 0, 50, 50, 0, 70, 90, 10, 50, 90, 20, 50, 80, 10, 60, 130, 20, 65, 70, 20, 65, 90, 30, 50, 110, 70, 65, 100
OFFSET
5,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^5.
MATHEMATICA
nmax = 82; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 100);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^5 )); // 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 A341796_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(5, x) ).list()
a=A341796_list(120); a[5:100] # G. C. Greubel, Jul 20 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 19 2021
STATUS
approved