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A125847 Denominator of volume of best symplectic packing of n balls in 4-dimensional ball. 4
1, 2, 4, 1, 5, 25, 64, 289, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Explanation, figure, table, references in Traynor. McDuff and Polterovich's existence proof of these packings in nonexplicit; they result from the symplectic blow-up operation. Explicit constructions for n = 8 and n = 9 are still unknown. Biran showed that A125846(n) = A125847(n) = 1 for all n>9.

REFERENCES

See A125846 for references.

LINKS

Table of n, a(n) for n=1..92.

FORMULA

A125846(n)/a(n) is maximal symplectic packing density with n balls, as calculated by McDuff and Polterovich.

EXAMPLE

For n = 1..9, densities are 1, 1/2, 3/4, 1, 4/5, 24/25, 63/64, 288/289, 1.

CROSSREFS

Cf. A125846.

See A030042/A030043 for an unreduced version.

Sequence in context: A090285 A286784 A047908 * A078886 A307796 A095247

Adjacent sequences:  A125844 A125845 A125846 * A125848 A125849 A125850

KEYWORD

nonn,frac

AUTHOR

Jonathan Vos Post, Dec 11 2006.

EXTENSIONS

Edited by N. J. A. Sloane, Feb 12 2021

STATUS

approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)