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%I #14 Sep 08 2022 08:45:28
%S 1,0,0,8,8,8,8,0,16,16,8,16,24,24,0,32,40,16,16,24,40,8,16,32,72,48,
%T 24,48,8,48,32,48,80,64,16,8,88,48,24,64,104,48,8,48,80,104,32,80,152,
%U 0,48,112,88,64,48,96,16,112,48,88,160,72,48,16,168,112,64,96,128,128,8,96,224
%N Theta series of 4-dimensional lattice S(7) with Gram matrix [ 3, 1, 0, -1; 1, 3, 1, 0; 0, 1, 3, 1; -1, 0, 1, 3 ].
%H John Cannon, <a href="/A125555/b125555.txt">Table of n, a(n) for n = 0..10000</a>
%e 1 + 8*q^3 + 8*q^4 + 8*q^5 + 8*q^6 + 16*q^8 + 16*q^9 + 8*q^10 + 16*q^11 + 24*q^12 + ...
%o (Magma) D := LatticeDatabase(); L := Lattice(D, 77); L:MAGMA; LatticeWithBasis(4, \[ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ], MatrixRing(IntegerRing(), 4) ! \[ 3, 1, 0, -1, 1, 3, 1, 0, 0, 1, 3, 1, -1, 0, 1, 3 ]) // _John Cannon_ [Note: running this code in the Magma Calculator causes an error at the "L:MAGMA" statement, and the code does not produce the terms of the sequence. - _Jon E. Schoenfield_, Feb 20 2018]
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 31 2007
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