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A341796 Number of ways to write n as an ordered sum of 5 nonzero tetrahedral numbers.

%I A341796 #11 Jul 20 2022 01:34:37
%S A341796 1,0,0,5,0,0,10,0,0,15,0,0,25,0,0,31,0,0,30,5,0,35,20,0,30,30,0,20,40,
%T A341796 0,20,65,0,10,65,0,5,70,10,5,90,30,0,70,30,1,85,40,0,80,60,0,50,50,0,
%U A341796 70,90,10,50,90,20,50,80,10,60,130,20,65,70,20,65,90,30,50,110,70,65,100
%N A341796 Number of ways to write n as an ordered sum of 5 nonzero tetrahedral numbers.
%H A341796 G. C. Greubel, <a href="/A341796/b341796.txt">Table of n, a(n) for n = 5..1000</a>
%F A341796 G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^5.
%t A341796 nmax = 82; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
%o A341796 (Magma)
%o A341796 R<x>:=PowerSeriesRing(Integers(), 100);
%o A341796 Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^5 )); // _G. C. Greubel_, Jul 20 2022
%o A341796 (SageMath)
%o A341796 def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
%o A341796 def A341796_list(prec):
%o A341796     P.<x> = PowerSeriesRing(ZZ, prec)
%o A341796     return P( f(5, x) ).list()
%o A341796 a=A341796_list(120); a[5:100] # _G. C. Greubel_, Jul 20 2022
%Y A341796 Cf. A000292, A023533, A023670, A282172, A282582, A340950, A341776, A341794, A341795, A341797, A341806, A341807, A341808, A341809.
%K A341796 nonn
%O A341796 5,4
%A A341796 _Ilya Gutkovskiy_, Feb 19 2021