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A059815
Let g_n be the ball packing n-width for the manifold torus X square; sequence gives numerator of (g_n/Pi)^2.
3
1, 1, 4, 4, 9, 16, 64, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1
OFFSET
1,3
LINKS
F. Miller Maley et al., Symplectic packings in cotangent bundles of tori, Experimental Mathematics, 9 (No. 3, 2000), 435-455.
FORMULA
From Colin Barker, Nov 06 2019: (Start)
G.f.: x*(1 + x + 3*x^2 + 3*x^3 + 5*x^4 + 12*x^5 + 55*x^6 - 15*x^7 - 62*x^8) / ((1 - x^2)).
a(n) = a(n-2) for n>=10.
a(n) = (3 - (-1)^n) / 2 for n>=8.
(End)
a(n) / A059816(n) = 2 / n, for n >= 8 [from Maley et al.]. - Sean A. Irvine, Oct 11 2022
EXAMPLE
1, 1, 4/9, 4/9, 9/25, 16/49, 64/225, 1/4, ...
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Feb 24 2001
EXTENSIONS
Edited by N. J. A. Sloane, May 23 2014
Duplicated a(8) removed and entry revised by Sean A. Irvine, Oct 11 2022
STATUS
approved