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%I #19 Jun 25 2017 02:48:18
%S 0,1,1,1,0,0,1,1,1,2,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,3,0,1,1,1,0,0,
%T 0,1,1,0,1,1,0,1,1,0,1,0,0,2,2,0,1,1,0,1,1,3,1,0,0,2,1,0,1,2,0,0,1,0,
%U 0,0,0,2,1,0,1,1,0,0,1,0,3,0,0,6,0,0,0,0,0,0,4,0,1,0,0,3,1,0,0,1,0,1,1,1,0,0,0,3,1,3,1,3,0,0,0,0,2,0,0,3,1,0,0,1,1,0,1,4,1,0,0,0,2,0,0,0,0,0,1,0,0,0,0,2,0,0,2,1,0,0,1
%N Number of Hamiltonian symmetric trivalent (or cubic) connected graphs on 2n nodes (the Foster census).
%C a(n) = A059282(n) for n <= 5000 except a(5) and a(14) which are one less. This corresponds to the fact that the Petersen and Coxeter graphs are non-Hamiltonian. [Comment updated by Marston Conder, May 08 2017. See comment in A059282 for further information. - _N. J. A. Sloane_, May 09 2017]
%H Marston Conder, <a href="/A091430/b091430.txt">Table of n, a(n) for n = 1..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SymmetricCubicGraph.html">Symmetric Cubic Graph</a>
%Y Cf. A059282.
%K nonn
%O 1,10
%A _Eric W. Weisstein_, Jan 06 2004
%E Corrected and extended by _N. J. A. Sloane_, May 09 2017, using Marston Conder's b-file
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