cp's OEIS Frontend

A340481 Number of ways to write n as an ordered sum of 5 squares of positive integers.

%I A340481 #14 Aug 09 2021 08:48:18
%S A340481 1,0,0,5,0,0,10,0,5,10,0,20,5,0,30,6,10,20,20,30,5,30,30,20,35,10,60,
%T A340481 45,0,60,50,30,45,50,60,70,35,30,110,50,31,110,80,80,50,70,120,70,75,
%U A340481 90,140,110,20,140,160,60,135,120,120,180,40,130,230,80,120,170,200,155,85,200,190
%N A340481 Number of ways to write n as an ordered sum of 5 squares of positive integers.
%H A340481 Alois P. Heinz, <a href="/A340481/b340481.txt">Table of n, a(n) for n = 5..20000</a>
%H A340481 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A340481 G.f.: (theta_3(x) - 1)^5 / 32, where theta_3() is the Jacobi theta function.
%p A340481 b:= proc(n, t) option remember;
%p A340481       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340481       `if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
%p A340481     end:
%p A340481 a:= n-> b(n, 5):
%p A340481 seq(a(n), n=5..75);  # _Alois P. Heinz_, Jan 31 2021
%t A340481 nmax = 75; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^5/32, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A340481 Cf. A000132, A000290, A010052, A025429, A038671, A063691, A063725, A063730, A340905, A340906, A340915, A340946, A340947.
%Y A340481 Column k=5 of A337165.
%K A340481 nonn,look
%O A340481 5,4
%A A340481 _Ilya Gutkovskiy_, Jan 31 2021