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 A181772 Kissing numbers for the laminated lattices Lambda(1), Lambda(2), Lambda(8), Lambda(24). 0
 2, 6, 240, 196560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Given on p. 8 of Dixon, with "coincidence" involving Fibonacci numbers. Since there is no indication of how the sequence 1,2,8,24 might be extended, I have marked this as "fini" and "full". - N. J. A. Sloane, Nov 12 2010 Let x = {1, 2, 8, 24}. Then (Lambda_x/x + 1)^2 - 1 = {8, 15, 960, 67092480} and is either a cake number (A000125) or the product of consecutive cake numbers. For instance, 960 = 1 * 2 * 4 * 8 * 15 = (Lambda_8/8 + 1)^2 - 1 and 67092480 = 1 * 2 * 4 * 8 * 15 * 26 * 42 * 64 = (Lambda_24/24 + 1)^2 - 1. This is interesting, at least in part, since x^2 = {1, 4, 64, 576} is also a cake number. - Raphie Frank, Dec 06 2012 REFERENCES J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Chap. 6. LINKS Geoffrey Dixon, Integral Octonions, Octonion XY-Product, and the Leech Lattice, Nov 11, 2010. CROSSREFS Cf. A002336. Sequence in context: A332692 A100359 A206033 * A183398 A052342 A199125 Adjacent sequences:  A181769 A181770 A181771 * A181773 A181774 A181775 KEYWORD nonn,fini,full AUTHOR EXTENSIONS Definition rewritten by N. J. A. Sloane, Nov 12 2010 STATUS approved

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Last modified June 4 01:54 EDT 2020. Contains 334812 sequences. (Running on oeis4.)