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A125847
Denominator of volume of best symplectic packing of n balls in 4-dimensional ball.
5
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
OFFSET
1,2
COMMENTS
Biran showed that A125846(n) = A125847(n) = 1 for all n >= 9.
REFERENCES
See A125846 for references.
FORMULA
A125846(n)/a(n) is maximal symplectic packing density with n balls, as calculated by McDuff and Polterovich.
G.f.: x*(1 + x + 2*x^2 - 3*x^3 + 4*x^4 + 20*x^5 + 39*x^6 + 225*x^7 - 288*x^8)/(1 - x). - Elmo R. Oliveira, Aug 04 2024
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
KEYWORD
nonn,frac,easy
AUTHOR
Jonathan Vos Post, Dec 11 2006
EXTENSIONS
Edited by N. J. A. Sloane, Feb 12 2021
STATUS
approved