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A317965 Representation numbers (or theta series) for either one of Schiemann's pair of four-dimensional positive definite quadratic forms with the same representation numbers. 1
1, 0, 2, 0, 4, 6, 10, 6, 12, 6, 6, 8, 10, 8, 10, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of ways either form represents 2n.

REFERENCES

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

Earnest, A. G., and G. Nipp. "On the theta series of positive quaternary quadratic forms." CR Math. Rep. Acad. Sci. Canada 13 (1991): 33-38. See p. 36.

Schiemann, Alexander. "Ein Beispiel positiv definiter quadratischer Formen der Dimension 4 mit gleichen Darstellungszahlen." Archiv der Mathematik, 54.4 (1990): 372-375.

LINKS

Table of n, a(n) for n=0..15.

J. H. Conway and N. J. A. Sloane, Four-Dimensional Lattices With the Same Theta Series, Duke Math. J., 66 (International Mathematics Research Notices Number 4) (1992), pp. 93-96. (Pages are in reverse order)

CROSSREFS

Sequence in context: A343468 A287846 A085623 * A190791 A002885 A344769

Adjacent sequences:  A317962 A317963 A317964 * A317966 A317967 A317968

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Aug 26 2018

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)