cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A320189 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 8*d^2 = n.

This page as a plain text file.
%I A320189 #15 Oct 30 2018 03:36:07
%S A320189 1,2,2,6,6,4,12,4,4,18,4,20,30,12,36,24,10,32,14,24,48,32,36,40,24,18,
%T A320189 28,34,36,60,60,28,28,40,16,56,78,44,108,68,8,72,24,40,144,60,72,112,
%U A320189 30,46,42,64,84,116,120,40,72,84,28,116,96,60,180,68,34,120,60,64,192,80
%N A320189 Number of integer solutions to a^2 + 2*b^2 + 3*c^2 + 8*d^2 = n.
%C A320189 a(n) > 0 for n >= 0.
%H A320189 Seiichi Manyama, <a href="/A320189/b320189.txt">Table of n, a(n) for n = 0..10000</a>
%F A320189 G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^3) * theta_3(q^8).
%t A320189 CoefficientList[Series[Product[EllipticTheta[3, 0, q^k], {k, 1, 3}]*EllipticTheta[3,0,q^8], {q, 0, 80}], q] (* _G. C. Greubel_, Oct 29 2018 *)
%o A320189 (PARI) q='q+O('q^80); Vec(prod(k=1,3, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )*eta(q^(16))^5/(eta(q^8)* eta(q^(32)))^2 ) \\ _G. C. Greubel_, Oct 29 2018
%Y A320189 Cf. A320138, A320139, A320140, A033712, A320188, A320190, A320191.
%K A320189 nonn
%O A320189 0,2
%A A320189 _Seiichi Manyama_, Oct 07 2018