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A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.

%I A341806 #9 Jul 20 2022 01:35:47
%S A341806 1,0,0,7,0,0,21,0,0,42,0,0,77,0,0,126,0,0,168,7,0,211,42,0,252,105,0,
%T A341806 252,182,0,245,315,0,231,469,0,175,574,21,140,735,105,105,854,210,56,
%U A341806 875,315,42,987,525,21,952,693,7,882,840,42,924,1155,140,770,1260,211,749,1470
%N A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.
%H A341806 G. C. Greubel, <a href="/A341806/b341806.txt">Table of n, a(n) for n = 7..1000</a>
%F A341806 G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^7.
%t A341806 nmax = 72; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
%o A341806 (Magma)
%o A341806 R<x>:=PowerSeriesRing(Integers(), 80);
%o A341806 Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^7 )); // _G. C. Greubel_, Jul 19 2022
%o A341806 (SageMath)
%o A341806 def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
%o A341806 def A341806_list(prec):
%o A341806     P.<x> = PowerSeriesRing(ZZ, prec)
%o A341806     return P( f(7, x) ).list()
%o A341806 a=A341806_list(100); a[7:81] # _G. C. Greubel_, Jul 19 2022
%Y A341806 Cf. A000292, A023533, A023670, A282582, A340952, A341778, A341794, A341795, A341796, A341797, A341807, A341808, A341809.
%K A341806 nonn
%O A341806 7,4
%A A341806 _Ilya Gutkovskiy_, Feb 20 2021