A059812 Let g_n be the ball packing n-width for the manifold torus X interval; sequence gives denominator of (g_n/Pi)^2.

1, 4, 4, 4, 25, 25, 64, 289, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64

Offset

1,2

Links

Table of n, a(n) for n=1..64.

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 (2,-1).

Formula

From Colin Barker, Nov 06 2019: (Start)

G.f.: x*(1 + 2*x - 3*x^2 + 21*x^4 - 21*x^5 + 39*x^6 + 186*x^7 - 505*x^8 + 281*x^9) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>10.

a(n) = n 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. A059811, A059813, A059814, A059815, A059816, A059817, A059818.

Sequence in context: A303397 A024949 A362374 * A077725 A217940 A353000

Adjacent sequences: A059809 A059810 A059811 * A059813 A059814 A059815

Keyword

nonn,frac,easy

Author

N. J. A. Sloane, Feb 24 2001

Extensions

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

Status

approved