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A004026 Number of perfect quadratic forms or lattices in dimension n.
(Formerly M0862)
7
1, 1, 1, 2, 3, 7, 33, 10916 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

D.-O. Jaquet, Classification des reseaux dans R^7 (via la notion de formes parfaites), Journees Arithmetiques, 1989 (Luminy, 1989). Asterisque No. 198-200 (1991), 7-8, 177-185 (1992).

J. Martinet, Les reseaux parfaits des espaces Euclidiens, Masson, Paris, 1996, p. 175.

J. Martinet, Perfect Lattices in Euclidean Spaces, Springer-Verlag, NY, 2003.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. Schürmann, Enumerating perfect forms, Contemporary Math., 493 (2009), 359-377. [From N. J. A. Sloane, Jan 21 2010]

LINKS

Table of n, a(n) for n=1..8.

J. H. Conway and N. J. A. Sloane, Low-dimensional lattices III: perfect forms, Proc. Royal Soc. London, A 418 (1988), 43-80.

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 3rd edition, 1999, see Preface to 3rd Ed., especially the page that was omitted by the publisher between pages xx and xxi!

Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin, Complete list of perfect forms in dimension 8

M. Dutour Sikiric, A. Schürmann and F. Vallentin, Classification of eight-dimensional perfect forms, arXiv:math/0609388 [math.NT], 2006-2009.

M. Dutour Sikiric, A. Schürmann and F. Vallentin, Classification of eight-dimensional perfect forms, Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 21-32

D.-O. Jaquet and F. Sigrist, Formes quadratiques contiguës à D_7, C. R. Acad. Sci. Paris Ser. I Math. 309 (1989), no. 10, 641-644.

G. Nebe, Review of J. Martinet, Perfect Lattices in Euclidean Spaces, Bull. Amer. Math. Soc., 41 (No. 4, 2004), 529-533.

A. Schürmann, Enumerating perfect forms, International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms, 2007.

A. Schürmann, Enumerating perfect forms, arXiv:0901.1587 [math.NT], 2009.

B. Venkov, Reseaux et designs spheriques, pp. 10-86 in Reseaux Euclidiens, Designs Spheriques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathematiques, Geneva, 2001.

CROSSREFS

Cf. A033689, A065535, A065536, A037075, A122079, A122080.

Sequence in context: A057677 A032148 A101484 * A135907 A027624 A165744

Adjacent sequences:  A004023 A004024 A004025 * A004027 A004028 A004029

KEYWORD

hard,more,nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(8) from the work of Mathieu Dutour Sikiric, Achill Schuermann and Frank Vallentin, Oct 05 2005

STATUS

approved

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Last modified June 24 01:22 EDT 2018. Contains 311819 sequences. (Running on oeis4.)