A306434 Theta series of 10-dimensional integral lattice O_10.

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

Table of n, a(n) for n=1..38.

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

Adjacent sequences: A306431 A306432 A306433 * A306435 A306436 A306437

Keyword

nonn

Author

Josiah Park, Feb 15 2019

Status

approved