|
%I #13 Feb 17 2022 07:25:12
%S 1,0,30,30,0,132,90,0,270,140,0,420,270,0,600,360,0,840,330,0,1092,
%T 660,0,1200,810,0,1500,570,0,1980,1020,0,2190,1260,0,2280,1100,0,2460,
%U 1560,0,3360,1620,0,3780,1452,0,3360,2190,0,3930,2340,0,4620,1710,0,5400,2940
%N Theta series of 5-dimensional lattice A_5^{+3}.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110 and 116.
%H John Cannon, <a href="/A125564/b125564.txt">Table of n, a(n) for n = 0..5000</a>
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1098/rspa.1988.0072">Low-Dimensional Lattices I: Quadratic Forms of Small Determinant</a>, Proc. Royal Soc. London, Series A, 418 (1988), 17-41.
%H LMFDB, <a href="https://lmfdb.org/Lattice/5.162.12.1.1">Integral lattice 5.162.12.1.1</a>
%H G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/P5.2.html">Home page for this lattice</a>
%e 1 + 30*q^4 + 30*q^6 + 132*q^10 + 90*q^12 + 270*q^16 + 140*q^18 + 420*q^22 + ...
%t al[n_, l_, p_, nn_] := Sum[Exp[-2 Pi I k l/n] EllipticTheta[3, Pi k/n, q^p]^n, {k, n}] / n / Sum[q^(p n (m + l/n)^2), {m, -nn, nn}] + O[q]^nn;
%t as[n_, s_, nn_] := CoefficientList[FullSimplify[Normal@Sum[al[n, l, n/s, nn], {l, s, n, s}]], q];
%t as[6, 1, 30] (*A023917*)
%t as[6, 2, 30][[;; ;; 2]] (*this sequence*)
%t as[6, 3, 30] (*A125561*)
%t (* _Andrey Zabolotskiy_, Feb 17 2022 *)
%Y Cf. A008445, A125561, A023917.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 31 2007
%E Typo in name corrected by _Andrey Zabolotskiy_, Feb 16 2022
|
