%I A003699
%S A003699 1,6,22,82,306,1142,4262,15906,59362,221542,826806,3085682,
%T A003699 11515922,42978006,160396102,598606402,2234029506,8337511622,
%U A003699 31116016982,116126556306,433390208242,1617434276662,6036346898406
%N A003699 Number of Hamilton cycles in C_4 X P_n.
%D A003699 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003699 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number 
               of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary 
               version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A003699 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A003699 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A003699 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting 
               Hamilton cycles in product graphs</a>
%F A003699 n>1, a(n) = ceiling((1-sqrt(1/3))*(2+sqrt(3))^n); recurrence: a(1) = 
               1, a(2) = 6, a(3) = 22 and for n>3 a(n) = 4*a(n-1)-a(n-2) - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Mar 28 2003
%F A003699 O.g.f.: -x*(-1-2*x+x^2)/(1-4*x+x^2) = -x-2+(-6*x+2)/(1-4*x+x^2) . - R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
%Y A003699 First differences of A052530 and A071954.
%Y A003699 Equals 2 * A001835(n), n>1.
%Y A003699 Sequence in context: A032195 A111566 A051945 this_sequence A047124 A046365 
               A078418
%Y A003699 Adjacent sequences: A003696 A003697 A003698 this_sequence A003700 A003701 
               A003702
%K A003699 nonn
%O A003699 1,2
%A A003699 Frans Faase (Frans_LiXia(AT)wxs.nl)