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A306434
Theta series of 10-dimensional integral lattice O_10.
0
1, 0, 0, 80, 270, 432, 960, 2160, 3240, 5360, 8640, 10800, 17790, 25920, 25920, 41232, 62910, 60480, 81600, 118800, 124416, 159760, 198720, 203040, 287160, 354240, 311040, 433760, 596700, 516240, 619200, 840240, 806760, 969360, 1140480, 1089504, 1465710, 1702080
OFFSET
1,4
COMMENTS
Theta series terms of shorter Coxeter-Todd lattice.
LINKS
G. Nebe and N. J. A. Sloane, The Lattice O_10
FORMULA
See Magma program.
PROG
(Magma)
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]]);
L:=LatticeWithGram(A);
T<q>:=ThetaSeries(L, 37);
S:=[];
for i in [0 .. 37] do S cat:= [Coefficient(T, i)]; end for;
S;
CROSSREFS
Cf. A029770.
Sequence in context: A203348 A235098 A235091 * A234890 A157912 A234883
KEYWORD
nonn
AUTHOR
Josiah Park, Feb 15 2019
STATUS
approved