A059816 - OEIS

A059816

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

1, 1, 9, 9, 25, 49, 225, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 16, 33, 17, 35, 18, 37, 19, 39, 20, 41, 21, 43, 22, 45, 23, 47, 24, 49, 25, 51, 26, 53, 27, 55, 28, 57, 29, 59, 30, 61, 31, 63, 32, 65, 33, 67, 34

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..68.

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

FORMULA

For n>=8, a(2n+1) = 2n+1, a(2n) = n. - Ralf Stephan, May 29 2004

From Colin Barker, Nov 06 2019: (Start)

G.f.: x*(1 + x + 7*x^2 + 7*x^3 + 8*x^4 + 32*x^5 + 184*x^6 - 85*x^7 - 416*x^8 + 46*x^9 + 218*x^10) / ((1 - x)^2*(1+x)^2).

a(n) = 2*a(n-2) - a(n-4) for n>=11.

a(n) = (1/4)*(3 - (-1)^n)*(n-1) for n>=8.