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Let g_n be the ball packing n-width for the manifold torus X interval; sequence gives numerator of (g_n/Pi)^2.
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%I #21 Oct 11 2022 06:36:24

%S 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,

%T 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,

%U 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

%N Let g_n be the ball packing n-width for the manifold torus X interval; 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_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

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

%F G.f.: x*(1 + 3*x^4 + 5*x^6 + 27*x^7 - 35*x^8) / (1 - x).

%F a(n) = a(n-1) for n>9.

%F a(n) = 1 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. A059812, A059813, A059814, A059815, A059816, A059817, A059818.

%K nonn,frac,easy

%O 1,5

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

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