A059815 Let g_n be the ball packing n-width for the manifold torus X square; sequence gives numerator of (g_n/Pi)^2.

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

Table of n, a(n) for n=1..86.

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

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, signature (0, 1).

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, ...

Prog

(PARI) a(n)=if(n>7, 1+n%2, [1, 1, 4, 4, 9, 16, 64][n]) \\ Charles R Greathouse IV, May 27 2026

Crossrefs

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

Sequence in context: A263727 A133037 A061886 * A202670 A203003 A377044

Adjacent sequences: A059812 A059813 A059814 * A059816 A059817 A059818

Keyword

nonn,frac,easy

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