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%I #22 Jun 29 2023 16:22:15
%S 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,
%T 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,
%U 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1
%N Let g_n be the ball packing n-width for the manifold torus X square; sequence gives numerator 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 (0, 1).
%F From _Colin Barker_, Nov 06 2019: (Start)
%F 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)).
%F a(n) = a(n-2) for n>=10.
%F a(n) = (3 - (-1)^n) / 2 for n>=8.
%F (End)
%F a(n) / A059816(n) = 2 / n, for n >= 8 [from Maley et al.]. - _Sean A. Irvine_, Oct 11 2022
%e 1, 1, 4/9, 4/9, 9/25, 16/49, 64/225, 1/4, ...
%Y Cf. A059812, A059813, A059814, A059816, A059817, A059818.
%K nonn,frac
%O 1,3
%A _N. J. A. Sloane_, Feb 24 2001
%E Edited by _N. J. A. Sloane_, May 23 2014
%E Duplicated a(8) removed and entry revised by _Sean A. Irvine_, Oct 11 2022
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