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 A029680 Theta series of quadratic form with Gram matrix [ 4, 2, 2; 2, 4, 1; 2, 1, 6 ]. 1

%I #18 Jul 17 2014 21:54:42

%S 1,0,6,4,4,0,14,4,6,8,2,0,20,8,12,4,16,0,26,0,0,8,8,4,42,0,20,16,12,8,

%T 0,8,14,16,20,4,36,0,20,8,6,8,52,4,8,0,12,12,52,8,6,16,24,8,46,0,20,8,

%U 20,8,16,8,20,12,28,0,64,12,16,32,0,8,58,8,20,4,16,8,60,0,0,24,44,4,40,0,20

%N Theta series of quadratic form with Gram matrix [ 4, 2, 2; 2, 4, 1; 2, 1, 6 ].

%C This is the digonal F lattice (the even holotype) of dimension 3.

%H John Cannon, <a href="/A029680/b029680.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) = coefficient of q^2n in theta3(q)*theta3(q^3)*theta3(q^5). Theta series of even sublattice of Z+sqrt(3)Z+sqrt(5)Z - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 07 2002 [corrected by _Michael Somos_, Apr 05 2012]

%e 1 + 6*x^2 + 4*x^3 + 4*x^4 + 14*x^6 + 4*x^7 + 6*x^8 + 8*x^9 + 2*x^10 + ...

%e 1 + 6*q^4 + 4*q^6 + 4*q^8 + 14*q^12 + 4*q^14 + 6*q^16 + 8*q^18 + 2*q^20 + ...

%o (PARI) {a(n) = if( n<1, n==0, qfrep( [ 4, 2, 2; 2, 4, 1; 2, 1, 6], n, 1)[n] * 2 )} /* _Michael Somos_, Apr 05 2012 */

%K nonn

%O 0,3

%A _N. J. A. Sloane_.

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Last modified May 28 23:06 EDT 2023. Contains 363028 sequences. (Running on oeis4.)