A015160 - OEIS

A015160

Theta series of 17-dimensional lattice Q_17(6)^{+3}.

1, 0, 0, 0, 0, 1020, 2040, 0, 34782, 41956, 0, 376992, 362406, 0, 2306832, 1933920, 0, 9891384, 7591792, 0, 33439476, 24124428, 0, 95442624, 65640978, 0, 239451936, 158815904, 0, 542842980, 350243520, 0, 1135694622, 715382916, 0, 2225152032, 1373241708, 0, 4123291248, 2505490464, 0, 7286817984, 4367865216, 0, 12375237108, 7321237204, 0, 20304913152, 11884992774, 0, 32294964192, 18736213536

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..51.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices II: Subgroups of GL(n,Z), Proc. Royal Soc. London, A 419 (1988), 29-68.

Gheorghe Coserea, Gram matrix.

G. Nebe and N. J. A. Sloane, Home page for this lattice

W. Plesken, Finite Unimodular Groups of Prime Degree and Circulants, J. Algebra, vol. 97 (1985), pp. 286-312.

EXAMPLE

1 + 1020*q^10 + 2040*q^12 + 34782*q^16 + 41956*q^18 + 376992*q^22 + 362406*q^24 + 2306832*q^28 + 1933920*q^30 + ...

PROG

(PARI) \\ system("wget https://oeis.org/A015160/a015160.txt");

g = matconcat(read("a015160.txt")~);

seq(N, g, flag=0) = concat(1, 2*Vec(qfrep(g, N, flag)));

seq(20, g, 1) \\ Gheorghe Coserea, Nov 28 2018

(PARI)

GramMatrix()={my(p=[10, -2, -5, 1, 4, 1, -5, 1, 1, 1, 1, -5, 1, 4, 1, -5, -2]); matrix(#p, #p, i, j, p[(i-j) %#p + 1])}

a(n)={if(n==0, 1, 2*qfrep(GramMatrix(), n, 1)[n])} \\ Andrew Howroyd, Nov 29 2018

CROSSREFS

Cf. A015158, A015159, A015161, A015162, A015163, A015164, A015165.

Sequence in context: A340872 A104444 A157510 * A102925 A216115 A024020

Adjacent sequences: A015157 A015158 A015159 * A015161 A015162 A015163

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Gheorghe Coserea, Nov 28 2018

STATUS

approved