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A306434 Theta series of 10-dimensional integral lattice O_10. 0

%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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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)