A054908 - OEIS

A054908

Number of n-dimensional odd unimodular lattices (or quadratic forms) containing no vectors of norm 1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 4, 3, 12, 12, 28, 49, 156, 368, 1901, 14493, 357003

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OFFSET

0,19

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 49.

LINKS

Bill Allombert and Gaëtan Chenevier, Unimodular Hunting II, arXiv:2410.19569 [math.NT], 2024.

Gaëtan Chenevier, Unimodular Hunting, arXiv:2410.18788 [math.NT], 2024.

FORMULA

If 8 divides n, then a(n) = A054907(n) - A054909(n/8), otherwise a(n) = A054907(n). - Robin Visser, Jan 24 2025

CROSSREFS

KEYWORD

nonn,nice,more,hard

AUTHOR

EXTENSIONS

a(26)-a(28) added from Bill Allombert's and Gaëtan Chenevier's computations by Robin Visser, Jan 24 2025

STATUS

approved