%I #37 Sep 08 2022 08:46:21
%S 1,0,0,80,270,432,960,2160,3240,5360,8640,10800,17790,25920,25920,
%T 41232,62910,60480,81600,118800,124416,159760,198720,203040,287160,
%U 354240,311040,433760,596700,516240,619200,840240,806760,969360,1140480,1089504,1465710,1702080
%N Theta series of 10-dimensional integral lattice O_10.
%C Theta series terms of shorter Coxeter-Todd lattice.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/O10_mod.html">The Lattice O_10</a>
%F See Magma program.
%o (Magma)
%o A:=Matrix([[3, -1, -1, -1, -1, 1, 0, -1, -1, 1], [-1, 3, -1, 1, 0, -1, 1, 1, -1, 1], [-1, -1, 3, 1, 0, -1, -1, 0, 1, -1], [-1, 1, 1, 3, -1, -1, -1, 1, 1, 0], [-1,0, 0, -1, 3, -1, 1, -1, 0, -1], [1, -1, -1, -1, -1, 3, -1, 0, 0, 1], [0, 1, -1, -1, 1, -1, 3, -1, -1, 0], [-1, 1, 0, 1, -1, 0, -1, 3, 1, 1], [-1, -1, 1, 1, 0, 0, -1, 1, 3, -1], [1, 1, -1, 0, -1, 1, 0, 1, -1, 3]]);
%o L:=LatticeWithGram(A);
%o T<q>:=ThetaSeries(L,37);
%o S:=[];
%o for i in [0 .. 37] do S cat:= [Coefficient(T,i)]; end for;
%o S;
%Y Cf. A029770.
%K nonn
%O 1,4
%A _Josiah Park_, Feb 15 2019
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