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A341807 Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.

%I A341807 #12 Jul 20 2022 01:35:50
%S A341807 1,0,0,8,0,0,28,0,0,64,0,0,126,0,0,224,0,0,336,8,0,456,56,0,589,168,0,
%T A341807 672,336,0,708,616,0,728,1016,0,658,1400,28,560,1856,168,476,2352,420,
%U A341807 336,2632,728,238,2968,1260,168,3192,1904,84,3096,2464,112,3192,3360,308,3024,4144
%N A341807 Number of ways to write n as an ordered sum of 8 nonzero tetrahedral numbers.
%H A341807 G. C. Greubel, <a href="/A341807/b341807.txt">Table of n, a(n) for n = 8..1000</a>
%F A341807 G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^8.
%t A341807 nmax = 70; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
%o A341807 (Magma)
%o A341807 R<x>:=PowerSeriesRing(Integers(), 80);
%o A341807 Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..70]])^8 )); // _G. C. Greubel_, Jul 19 2022
%o A341807 (SageMath)
%o A341807 def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..8) ) )^m
%o A341807 def A341807_list(prec):
%o A341807     P.<x> = PowerSeriesRing(ZZ, prec)
%o A341807     return P( f(8, x) ).list()
%o A341807 a=A341807_list(100); a[8:81] # _G. C. Greubel_, Jul 19 2022
%Y A341807 Cf. A000292, A023533, A023670, A282582, A340953, A341791, A341794, A341795, A341796, A341797, A341806, A341808, A341809.
%K A341807 nonn
%O A341807 8,4
%A A341807 _Ilya Gutkovskiy_, Feb 20 2021