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A015162 Theta series of 17-dimensional lattice Q'_17(6). 8

%I #30 Dec 02 2018 08:14:58

%S 1,0,1326,31552,240618,1452480,5030028,18128256,43527174,119299200,

%T 232127928,537564480,910537442,1881950592,2894860164,5501926784,

%U 7880557842,14072683776,19054928890,32409323328,42013951980,68622996416,85866810348,135824277120,164834073388,253845438336,300583037448

%N Theta series of 17-dimensional lattice Q'_17(6).

%H J. H. Conway and N. J. A. Sloane, <a href="https://www.jstor.org/stable/2398331">Low-Dimensional Lattices II: Subgroups of GL(n,Z)</a>, Proc. Royal Soc. London, A 419 (1988), 29-68.

%H Gheorghe Coserea, <a href="/A015162/a015162.txt">Gram matrix</a>.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Qp1761.html">Home page for this lattice</a>

%H W. Plesken, <a href="https://core.ac.uk/download/pdf/82549703.pdf">Finite Unimodular Groups of Prime Degree and Circulants</a>, J. Algebra, vol. 97 (1985), pp. 286-312.

%e 1 + 1326*q^4 + 31552*q^6 + 240618*q^8 + 1452480*q^10 + 5030028*q^12 + 18128256*q^14 + 43527174*q^16 + 119299200*q^18 + ...

%o (PARI) \\ system("wget https://oeis.org/A015162/a015162.txt");

%o g = matconcat(read("a015162.txt")~);

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

%o seq(10, g, 1) \\ _Gheorghe Coserea_, Nov 28 2018

%o (PARI)

%o GramMatrix()={my(p=[4, 1, -1, 1, 1, -1, 0, 2, 1, 1, 2, 0, -1, 1, 1, -1, 1]); matrix(#p, #p, i, j, p[(i-j) %#p + 1])}

%o a(n)={if(n==0, 1, 2*qfrep(GramMatrix(), n, 1)[n])} \\ _Andrew Howroyd_, Nov 29 2018

%Y Cf. A015158, A015159, A015160, A015161, A015163, A015164, A015165.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Gheorghe Coserea_, Dec 01 2018

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)