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%I #8 Jan 31 2021 20:18:31
%S 1,0,5,0,10,5,10,20,5,35,11,40,30,35,55,30,90,25,100,60,80,120,60,140,
%T 90,161,100,165,135,165,210,140,220,180,265,170,295,200,285,330,205,
%U 365,260,395,295,391,350,355,480,340,455,490,415,480,515,445,600,510,565,550,680,545,555
%N Number of ways to write n as an ordered sum of 5 nonzero triangular numbers.
%H Alois P. Heinz, <a href="/A340950/b340950.txt">Table of n, a(n) for n = 5..10000</a>
%F G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^5, where theta_2() is the Jacobi theta function.
%p b:= proc(n, k) option remember; local r, t, d; r, t, d:= $0..2;
%p if n=0 then `if`(k=0, 1, 0) else
%p while t<=n do r:= r+b(n-t, k-1); t, d:= t+d, d+1 od; r fi
%p end:
%p a:= n-> b(n, 5):
%p seq(a(n), n=5..67); # _Alois P. Heinz_, Jan 31 2021
%t nmax = 67; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y Cf. A000217, A008439, A010054, A053603, A053604, A319815, A340949, A340951, A340952, A340953, A340954, A340955.
%K nonn
%O 5,3
%A _Ilya Gutkovskiy_, Jan 31 2021
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