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A341809
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Number of ways to write n as an ordered sum of 10 nonzero tetrahedral numbers.
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6
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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
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OFFSET
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10,4
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 10..1000
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FORMULA
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G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^10.
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MATHEMATICA
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nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
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PROG
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(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
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CROSSREFS
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Cf. A000292, A023533, A023670, A282582, A340955, A341793, A341794, A341795, A341796, A341797, A341806, A341807, A341808.
Sequence in context: A288435 A287734 A064511 * A340947 A306934 A003785
Adjacent sequences: A341806 A341807 A341808 * A341810 A341811 A341812
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Feb 20 2021
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STATUS
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approved
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