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.
%I A046113 #29 Nov 15 2024 09:03:25
%S A046113 1,2,0,0,2,0,2,4,0,2,4,0,0,0,0,4,2,0,0,0,0,0,4,0,2,6,0,0,4,0,0,4,0,4,
%T A046113 0,0,2,0,0,0,4,0,4,0,0,0,0,0,0,6,0,0,0,0,2,8,0,0,4,0,4,0,0,4,2,0,0,0,
%U A046113 0,0,8,0,0,4,0,0,0,0,0,4,0,2,0,0,0,0,0,4,4,0,4,0,0
%N A046113 Coefficients in expansion of theta_3(q) * theta_3(q^6) in powers of q.
%C A046113 Number of representations of n as a sum of six times a square and a square. - _Ralf Stephan_, May 14 2007
%C A046113 a(n) < 2 if and only if n is in A002480. a(n) > 0 if and only if n is in A002481. - _Michael Somos_, Mar 01 2011
%D A046113 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
%H A046113 Seiichi Manyama, <a href="/A046113/b046113.txt">Table of n, a(n) for n = 0..10000</a>
%H A046113 A. Berkovich and H. Yesilyurt, <a href="https://arxiv.org/abs/math/0611300">Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms</a>, arXiv:math/0611300 [math.NT], 2016-2017.
%F A046113 G.f.: Sum_{ i, j = -oo..+oo } q^(i^2 + 6*j^2).
%F A046113 a(n) = A000377(n) + A115660(n). - _Michael Somos_, Mar 01 2011
%F A046113 a(0) = 1, a(n) = (1+(-1)^t)*b(n) for n > 0, where t is the number of prime factors of n, counting multiplicity, which are == 2,3,5,11 (mod 24), and b() is multiplicative with b(p^e) = (e+1) for primes p == 1,5,7,11 (mod 24) and b(p^e) = (1+(-1)^e)/2 for primes p == 13,17,19,23 (mod 24). (This formula is Corollary 4.2 in the Berkovich-Yesilyurt paper). - _Jeremy Lovejoy_, Nov 14 2024
%e A046113 G.f. = 1 + 2*x + 2*x^4 + 2*x^6 + 4*x^7 + 2*x^9 + 4*x^10 + 4*x^15 + 2*x^16 + ...
%t A046113 a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^6], {q, 0, n}]; (* _Michael Somos_, Apr 19 2015 *)
%o A046113 (PARI) {a(n) = my(G); if( n<0, 0, G = [ 1, 0; 0, 6]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n)), n))}; /* _Michael Somos_, Mar 01 2011 */
%Y A046113 Cf. A000377, A002480, A002481, A115660.
%K A046113 nonn
%O A046113 0,2
%A A046113 _N. J. A. Sloane_, May 18 2002