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A341797 Number of ways to write n as an ordered sum of 6 nonzero tetrahedral numbers.

%I A341797 #10 Jul 20 2022 01:35:29
%S A341797 1,0,0,6,0,0,15,0,0,26,0,0,45,0,0,66,0,0,76,6,0,90,30,0,96,60,0,80,90,
%T A341797 0,75,150,0,60,192,0,35,210,15,30,270,60,15,270,90,6,270,120,6,306,
%U A341797 195,0,240,210,1,246,270,20,240,360,60,180,330,60,216,450,80,210,435,120,216,360
%N A341797 Number of ways to write n as an ordered sum of 6 nonzero tetrahedral numbers.
%H A341797 G. C. Greubel, <a href="/A341797/b341797.txt">Table of n, a(n) for n = 6..1000</a>
%F A341797 G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^6.
%t A341797 nmax = 77; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 6] &
%o A341797 (Magma)
%o A341797 R<x>:=PowerSeriesRing(Integers(), 80);
%o A341797 Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^6 )); // _G. C. Greubel_, Jul 20 2022
%o A341797 (SageMath)
%o A341797 def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
%o A341797 def A341797_list(prec):
%o A341797     P.<x> = PowerSeriesRing(ZZ, prec)
%o A341797     return P( f(6, x) ).list()
%o A341797 a=A341797_list(100); a[6:81] # _G. C. Greubel_, Jul 20 2022
%Y A341797 Cf. A000292, A023533, A023670, A282582, A340951, A341777, A341794, A341795, A341796, A341797, A341806, A341807, A341808, A341809.
%K A341797 nonn
%O A341797 6,4
%A A341797 _Ilya Gutkovskiy_, Feb 19 2021