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A341809 Number of ways to write n as an ordered sum of 10 nonzero tetrahedral numbers. 6
1, 0, 0, 10, 0, 0, 45, 0, 0, 130, 0, 0, 300, 0, 0, 612, 0, 0, 1095, 10, 0, 1740, 90, 0, 2565, 360, 0, 3490, 930, 0, 4351, 1980, 0, 5130, 3790, 0, 5680, 6330, 45, 5820, 9540, 360, 5715, 13620, 1260, 5292, 17950, 2880, 4530, 22140, 5670, 3780, 26490, 10170, 2940, 29770, 15840 (list; graph; refs; listen; history; text; internal format)
OFFSET
10,4
LINKS
FORMULA
G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^10.
MATHEMATICA
nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 70);
Coefficients(R!( (&+[x^Binomial(j+2, 3): j in [1..70]])^10 )); // G. C. Greubel, Jul 18 2022
(Sage)
def f(m, x): return ( sum( x^(binomial(j+2, 3)) for j in (1..8) ) )^m
def A341809_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(10, x) ).list()
a=A341809_list(100); a[10:71] # G. C. Greubel, Jul 18 2022
CROSSREFS
Sequence in context: A288435 A287734 A064511 * A340947 A306934 A003785
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 20 2021
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)