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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 G. C. Greubel, Table of n, a(n) for n = 10..1000 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:=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. = PowerSeriesRing(ZZ, prec) return P( f(10, x) ).list() a=A341809_list(100); a[10:71] # G. C. Greubel, Jul 18 2022 CROSSREFS 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 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 20 2021 STATUS approved

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Last modified March 22 18:11 EDT 2023. Contains 361432 sequences. (Running on oeis4.)