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A341808 Number of ways to write n as an ordered sum of 9 nonzero tetrahedral numbers.

%I A341808 #10 Jul 19 2022 08:04:44
%S A341808 1,0,0,9,0,0,36,0,0,93,0,0,198,0,0,378,0,0,624,9,0,918,72,0,1269,252,
%T A341808 0,1597,576,0,1836,1134,0,2025,2025,0,2058,3096,36,1926,4356,252,1764,
%U A341808 5877,756,1470,7182,1512,1134,8388,2772,882,9576,4608,588,10035,6552,462
%N A341808 Number of ways to write n as an ordered sum of 9 nonzero tetrahedral numbers.
%H A341808 G. C. Greubel, <a href="/A341808/b341808.txt">Table of n, a(n) for n = 9..1000</a>
%F A341808 G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^9.
%t A341808 nmax = 66; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
%o A341808 (Magma)
%o A341808 R<x>:=PowerSeriesRing(Integers(), 70);
%o A341808 Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^9 )); // _G. C. Greubel_, Jul 18 2022
%o A341808 (SageMath)
%o A341808 def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
%o A341808 def A341808_list(prec):
%o A341808     P.<x> = PowerSeriesRing(ZZ, prec)
%o A341808     return P( f(9, x) ).list()
%o A341808 a=A341808_list(100); a[9:71] # _G. C. Greubel_, Jul 18 2022
%Y A341808 Cf. A000292, A023533, A023670, A282582, A340954, A341792, A341794, A341795, A341796, A341797, A341806, A341807, A341809.
%K A341808 nonn
%O A341808 9,4
%A A341808 _Ilya Gutkovskiy_, Feb 20 2021