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A341806
Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.
6
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
7,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^7.
MATHEMATICA
nmax = 72; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..20]])^7 )); // G. C. Greubel, Jul 19 2022
(SageMath)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..20) ) )^m
def A341806_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(7, x) ).list()
a=A341806_list(100); a[7:81] # G. C. Greubel, Jul 19 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 20 2021
STATUS
approved