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 A059815 Let g_n be the ball packing n-width for the manifold torus X square; sequence gives numerator of (g_n/Pi)^2. 3
 1, 1, 4, 4, 9, 16, 64, 1, 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, 2, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS F. Miller Maley et al., Symplectic packings in cotangent bundles of tori, Experimental Mathematics, 9 (No. 3, 2000), 435-455. FORMULA Conjectures 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 - 63*x^8 + x^9) / ((1 - x)*(1 + x)). a(n) = a(n-2) for n>10. a(n) = (3 + (-1)^n) / 2 for n>8. (End) EXAMPLE 1, 1, 4/9, 4/9, 9/25, 16/49, 64/225, 1/4, ... CROSSREFS Cf. A059812, A059813, A059814, A059816, A059817, A059818. Sequence in context: A263727 A133037 A061886 * A202670 A203003 A319646 Adjacent sequences:  A059812 A059813 A059814 * A059816 A059817 A059818 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Feb 24 2001 EXTENSIONS Edited by N. J. A. Sloane, May 23 2014 STATUS approved

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Last modified September 21 05:55 EDT 2020. Contains 337267 sequences. (Running on oeis4.)