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A008445 Theta series of A_5 lattice.

%I A008445 #25 Sep 08 2022 08:44:35
%S A008445 1,30,90,140,270,360,330,660,810,570,1020,1260,1100,1560,1620,1452,
%T A008445 2190,2340,1710,2940,3240,1920,3360,3960,2970,3930,4140,3920,5460,
%U A008445 4680,3360,5940,6570,4620,6180,7560,5130,7320,7920,5280,9180,8100,6600,10500,9900
%N A008445 Theta series of A_5 lattice.
%D A008445 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.
%H A008445 John Cannon, <a href="/A008445/b008445.txt">Table of n, a(n) for n = 0..5000</a>
%H A008445 LMFDB, <a href="http://www.lmfdb.org/Lattice/5.6.12.1.1">Integral Lattice A5</a>.
%e A008445 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 A008445 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 A008445 (Magma) L:=Lattice("A",5); T1<q> := ThetaSeries(L,120);
%o A008445 (PARI)
%o A008445 seq(N) = {
%o A008445   my(q=[2,-1,0,0,0; -1,2,-1,0,0; 0,-1,2,-1,0;
%o A008445         0,0, -1,2,-1; 0,0,0,-1,2]);
%o A008445   concat(1, 2*Vec(qfrep(q,N-1,1)));
%o A008445 };
%o A008445 seq(45) \\ _Gheorghe Coserea_, Nov 25 2018
%K A008445 nonn
%O A008445 0,2
%A A008445 _N. J. A. Sloane_