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.

A008424 Theta series of {D_9}* lattice.

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%I A008424 #19 Jul 24 2021 02:24:31
%S A008424 1,0,0,0,18,0,0,0,144,512,0,0,672,0,0,0,2034,4608,0,0,4320,0,0,0,7392,
%T A008424 18432,0,0,12672,0,0,0,22608,47616,0,0,34802,0,0,0,44640,101376,0,0,
%U A008424 60768,0,0,0,93984,193536,0,0,125280,0,0,0,141120,324096,0,0
%N A008424 Theta series of {D_9}* lattice.
%D A008424 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
%H A008424 Andy Huchala, <a href="/A008424/b008424.txt">Table of n, a(n) for n = 0..3000</a>
%H A008424 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds9.html">Home page for this lattice</a>
%F A008424 Theta series in terms of Jacobi theta series: (theta_2)^9 + (theta_3)^9. - _Sean A. Irvine_, Mar 28 2018
%e A008424 G.f. = 1 + 18*q^4 + 144*q^8 + ...
%o A008424 (PARI)
%o A008424 N=66;  q='q+O('q^N);
%o A008424 T3(q) = eta(q^2)^5 / ( eta(q)^2 * eta(q^4)^2 );
%o A008424 T2(q) = eta(q^4)^2 / eta(q^2);
%o A008424 Vec( T3(q^4)^9 + (2 * q * T2(q^4))^9 )
%o A008424 \\ _Joerg Arndt_, Mar 29 2018
%o A008424 (Magma)
%o A008424 L := Dual(Lattice("D", 9));
%o A008424 B := Basis(ThetaSeriesModularFormSpace(L), 100);
%o A008424 S := [ 1, 0, 0, 0, 18];
%o A008424 Coefficients(&+[B[i] * S[i] : i in [1..5]]); // _Andy Huchala_, Jul 24 2021
%Y A008424 Cf. A008431.
%K A008424 nonn,easy
%O A008424 0,5
%A A008424 _N. J. A. Sloane_
%E A008424 More terms from _Andy Huchala_, Jul 24 2021