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 A028997 #26 Jul 08 2025 19:00:24
%S A028997 1,0,8,8,16,8,24,0,40,16,40,16,72,24,8,32,80,16,88,24,104,8,80,32,152,
%T A028997 48,88,48,16,48,160,48,168,64,128,8,224,48,136,64,232,48,24,48,208,
%U A028997 104,160,80,328,0,200,112,248,64,272,96,40,112,192,88,416,72,208,16,336,112,320
%N A028997 Theta series of quadratic form with Gram matrix [ 4, 1, 0, 1; 1, 4, 1, 0; 0, 1, 4, -1; 1, 0, -1, 4 ].
%C A028997 Associated with permutations in Mathieu group M24 of shape (14)(7)(2)(1). - _Michael Somos_, Nov 22 2007
%H A028997 John Cannon, <a href="/A028997/b028997.txt">Table of n, a(n) for n = 0..5000</a>
%H A028997 M. Koike, <a href="http://projecteuclid.org/euclid.nmj/1118787871">Mathieu group M24 and modular forms</a>, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
%H A028997 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/QQF.4.c.html">Home page for this lattice</a>
%F A028997 G.f. is Fourier series of a weight 2 level 14 modular form. f(-1 / (14 t)) = 14 (t/i)^2 f(t) where q = exp(2 Pi i t). - _Michael Somos_, Nov 22 2007
%F A028997 Convolution of A030187 and A134782. - _Michael Somos_, Nov 22 2007
%e A028997 G.f. = 1 + 8*x^2 + 8*x^3 + 16*x^4 + 8*x^5 + 24*x^6 + 40*x^8 + 16*x^9 + 40*x^10 + ...
%e A028997 G.f. = 1 + 8*q^4 + 8*q^6 + 16*q^8 + 8*q^10 + 24*q^12 + 40*q^16 + 16*q^18 + 40*q^20 + ...
%t A028997 a[ n_] := With[{e1 = QPochhammer[ x] QPochhammer[ x^7], e2 = QPochhammer[ x^2] QPochhammer[ x^14]}, SeriesCoefficient[ e1^4 / e2^2 + 4 x e1 e2 + 8 x^2 e2^4 / e1^2, {x, 0, n}]]; (* _Michael Somos_, Apr 19 2015 *)
%o A028997 (PARI) {a(n) = my(A, B); if( n<0, 0, A = x * O(x^n); B = eta(x^2 + A) * eta(x^14 + A); A = eta(x + A) * eta(x^7 + A); polcoeff( A^4 / B^2 + 4 * x * A * B + 8 * x^2 * B^4 / A^2, n))}; /* _Michael Somos_, Nov 22 2007 */
%o A028997 (PARI) {a(n) = my(G); if( n<0, 0, G = [ 4, 1, 0, 1; 1, 4, 1, 0; 0, 1, 4, -1; 1, 0, -1, 4 ]; polcoeff( 1 + 2 * x * Ser(qfrep( G, n, 1)), n))}; /* _Michael Somos_, Nov 22 2007 */
%o A028997 (Magma) A := Basis( ModularForms( Gamma0(14), 2), 67); A[1] + 8*A[3] + 8*A[4]; /* _Michael Somos_, Apr 19 2015 */
%Y A028997 Cf. A030187, A134782.
%K A028997 nonn
%O A028997 0,3
%A A028997 _N. J. A. Sloane_