%I #21 Oct 11 2022 06:37:25

%S 1,4,4,4,25,25,64,289,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,

%T 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,

%U 48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64

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

%H F. Miller Maley et al., <a href="https://projecteuclid.org/euclid.em/1045604678">Symplectic packings in cotangent bundles of tori</a>, Experimental Mathematics, 9 (No. 3, 2000), 435-455.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Colin Barker_, Nov 06 2019: (Start)

%F 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.

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

%F a(n) = n for n>8.

%F (End)

%e 1, 1/4, 1/4, 1/4, 4/25, 4/25, 9/64, 36/289, 1/9, 1/10, ...

%Y Cf. A059811, A059813, A059814, A059815, A059816, A059817, A059818.

%K nonn,frac,easy

%O 1,2

%A _N. J. A. Sloane_, Feb 24 2001

%E Edited by _N. J. A. Sloane_, May 23 2014