A181772 - OEIS

%I #16 Nov 05 2025 15:22:19

%S 2,6,240,196560

%N Kissing numbers for the laminated lattices Lambda(1), Lambda(2), Lambda(8), Lambda(24).

%C Given on p. 8 of Dixon, with "coincidence" involving Fibonacci numbers.

%C 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

%C 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

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Chap. 6.

%H Geoffrey Dixon, <a href="https://arxiv.org/abs/1011.2541">Integral Octonions, Octonion XY-Product, and the Leech Lattice</a>, Nov 11, 2010.

%Y Cf. A002336.

%K nonn,fini,full

%O 1,1

%A _Jonathan Vos Post_

%E Definition rewritten by _N. J. A. Sloane_, Nov 12 2010