A059815 - OEIS

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

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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 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.