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A059811
Let g_n be the ball packing n-width for the manifold torus X interval; sequence gives numerator of (g_n/Pi)^2.
3
1, 1, 1, 1, 4, 4, 9, 36, 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, 1
OFFSET
1,5
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 + 3*x^4 + 5*x^6 + 27*x^7 - 35*x^8) / (1 - x).
a(n) = a(n-1) for n>9.
a(n) = 1 for n>8.
(End)
EXAMPLE
1, 1/4, 1/4, 1/4, 4/25, 4/25, 9/64, 36/289, 1/9, 1/10, ...
KEYWORD
nonn,frac,easy
AUTHOR
N. J. A. Sloane, Feb 24 2001
EXTENSIONS
Edited by N. J. A. Sloane, May 23 2014
STATUS
approved