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Theta series of A_5 lattice.
6

%I #25 Sep 08 2022 08:44:35

%S 1,30,90,140,270,360,330,660,810,570,1020,1260,1100,1560,1620,1452,

%T 2190,2340,1710,2940,3240,1920,3360,3960,2970,3930,4140,3920,5460,

%U 4680,3360,5940,6570,4620,6180,7560,5130,7320,7920,5280,9180,8100,6600,10500,9900

%N Theta series of A_5 lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.

%H John Cannon, <a href="/A008445/b008445.txt">Table of n, a(n) for n = 0..5000</a>

%H LMFDB, <a href="http://www.lmfdb.org/Lattice/5.6.12.1.1">Integral Lattice A5</a>.

%e 1 + 30*q^2 + 90*q^4 + 140*q^6 + 270*q^8 + 360*q^10 + 330*q^12 + 660*q^14 + 810*q^16 + 570*q^18 + 1020*q^20 + 1260*q^22 + 1100*q^24 + 1560*q^26 + 1620*q^28 + 1452*q^30 + 2190*q^32 + 2340*q^34 + 1710*q^36 + 2940*q^38 + 3240*q^40 + 1920*q^42 + 3360*q^44 + 3960*q^46 + 2970*q^48 + ...

%t terms = 45; f[q_] = LatticeData["A5", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; CoefficientList[s, q^2][[1 ;; terms]] (* _Jean-François Alcover_, Jul 04 2017 *)

%o (Magma) L:=Lattice("A",5); T1<q> := ThetaSeries(L,120);

%o (PARI)

%o seq(N) = {

%o my(q=[2,-1,0,0,0; -1,2,-1,0,0; 0,-1,2,-1,0;

%o 0,0, -1,2,-1; 0,0,0,-1,2]);

%o concat(1, 2*Vec(qfrep(q,N-1,1)));

%o };

%o seq(45) \\ _Gheorghe Coserea_, Nov 25 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_