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A341807
Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.
6
1, 0, 0, 8, 0, 0, 28, 0, 0, 64, 0, 0, 126, 0, 0, 224, 0, 0, 336, 8, 0, 456, 56, 0, 589, 168, 0, 672, 336, 0, 708, 616, 0, 728, 1016, 0, 658, 1400, 28, 560, 1856, 168, 476, 2352, 420, 336, 2632, 728, 238, 2968, 1260, 168, 3192, 1904, 84, 3096, 2464, 112, 3192, 3360, 308, 3024, 4144
OFFSET
8,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^8.
MATHEMATICA
nmax = 70; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..70]])^8 )); // G. C. Greubel, Jul 19 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..8) ) )^m
def A341807_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(8, x) ).list()
a=A341807_list(100); a[8:81] # G. C. Greubel, Jul 19 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 20 2021
STATUS
approved