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A059816 Let g_n be the ball packing n-width for the manifold torus X square; sequence gives denominator of (g_n/Pi)^2. 3
1, 1, 9, 9, 25, 49, 225, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 16, 33, 17, 35, 18, 37, 19, 39, 20, 41, 21, 43, 22, 45, 23, 47, 24, 49, 25, 51, 26, 53, 27, 55, 28, 57, 29, 59, 30, 61, 31, 63, 32, 65, 33, 67, 34 (list; graph; refs; listen; history; text; internal format)
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
For n>=8, a(2n+1) = 2n+1, a(2n) = n. - Ralf Stephan, May 29 2004
From Colin Barker, Nov 06 2019: (Start)
G.f.: x*(1 + x + 7*x^2 + 7*x^3 + 8*x^4 + 32*x^5 + 184*x^6 - 85*x^7 - 416*x^8 + 46*x^9 + 218*x^10) / ((1 - x)^2*(1+x)^2).
a(n) = 2*a(n-2) - a(n-4) for n>=11.
a(n) = (1/4)*(3 - (-1)^n)*(n-1) for n>=8.
(End)
A059815(n) / a(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
Sequence in context: A146367 A014725 A202208 * A339716 A111005 A076089
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

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)