A169719 Theta series of extremal lattice of dimension 14, level 7 and minimal norm 6.

1, 0, 0, 560, 2394, 9072, 26824, 71136, 158004, 306432, 599256, 1034208, 1784328, 2849616, 4489776, 6664896, 9985374, 14200704

Offset

0,4

Comments

The lattice has Gram matrix:

6

-2 6

2 -3 6

-3 0 1 6

-3 1 -2 3 6

-1 3 0 2 0 6

-1 2 -3 1 3 2 6

2 -2 0 -3 -3 -3 -3 6

-3 3 -1 1 1 3 0 -1 6

2 1 0 0 -2 1 1 1 -2 6

-2 3 0 1 2 2 2 -3 1 -1 6

-3 3 0 2 1 2 -1 -1 2 0 2 6

-3 3 -3 1 3 2 3 -2 3 0 1 2 6

2 1 2 -2 -1 1 0 -1 1 -1 1 0 -1 6

References

Scharlau, Rudolf and Schulze-Pillot, Rainer, Extremal lattices, in Algorithmic algebra and number theory (Heidelberg, 1997), 139-170, Springer, Berlin, 1999. [Here the existence of such a lattice is left open.]

Links

Table of n, a(n) for n=0..17.

Example

1 + 560*q^3 + 2394*q^4 + 9072*q^5 + 26824*q^6 + 71136*q^7 + 158004*q^8 + 306432*q^9 + 599256*q^10 + 1034208*q^11 + 1784328*q^12 + 2849616*q^13 + 4489776*q^14 + 6664896*q^15 + 9985374*q^16 + 14200704*q^17 + O(q^18)

Crossrefs

Sequence in context: A260290 A249839 A069243 * A104591 A318119 A364151

Adjacent sequences: A169716 A169717 A169718 * A169720 A169721 A169722

Keyword

nonn

Author

Boris Hemkemeier (bhemkemeier(AT)googlemail.com) and Rudolf Scharlau (Rudolf.Scharlau(AT)math.uni-dortmund.de), Apr 21 2010

Status

approved