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A004026 Number of perfect quadratic forms or lattices in dimension n.
(Formerly M0862)
6
1, 1, 1, 2, 3, 7, 33, 10916 (list; graph; refs; listen; history; internal format)
OFFSET

1,4

REFERENCES

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

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).

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

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

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

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

M. Dutour Sikiric, A. Schuermann and F. Vallentin, Classifiaction of eight-dimensional perfect forms, Preprint, 2006.

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

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

LINKS

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 Schuermann and Frank Vallentin, Complete list of perfect forms in dimension 8

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 A165744 A034900

Adjacent sequences:  A004023 A004024 A004025 * A004027 A004028 A004029

KEYWORD

hard,nonn,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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

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Last modified February 17 19:13 EST 2012. Contains 206085 sequences.