A059811 Let g_n be the ball packing n-width for the manifold torus X interval; sequence gives numerator of (g_n/Pi)^2.

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

Table of n, a(n) for n=1..93.

F. Miller Maley et al., Symplectic packings in cotangent bundles of tori, Experimental Mathematics, 9 (No. 3, 2000), 435-455.

Index entries for linear recurrences with constant coefficients, signature (1).

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, ...

Crossrefs

Cf. A059812, A059813, A059814, A059815, A059816, A059817, A059818.

Sequence in context: A117416 A174943 A173317 * A202409 A091016 A198025

Adjacent sequences: A059808 A059809 A059810 * A059812 A059813 A059814

Keyword

nonn,frac,easy

Author

N. J. A. Sloane, Feb 24 2001

Extensions

Edited by N. J. A. Sloane, May 23 2014

Status

approved