%I A003766
%S A003766 6,152,1608,15420,127980,1003360,7432708,53294540,371397240,
%T A003766 2537155684,17047659916,113102692016,742597784164,4835184613212,
%U A003766 31267479066856,201066698078244,1286998671857356,8206523391863296
%N A003766 Number of Hamiltonian paths in W_4 X P_n.
%D A003766 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003766 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 A003766 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A003766 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A003766 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting 
               Hamilton cycles in product graphs</a>
%F A003766 Faase gives a 16-term linear recurrence on his web page:
%F A003766 a(1) = 6,
%F A003766 a(2) = 152,
%F A003766 a(3) = 1608,
%F A003766 a(4) = 15420,
%F A003766 a(5) = 127980,
%F A003766 a(6) = 1003360,
%F A003766 a(7) = 7432708,
%F A003766 a(8) = 53294540,
%F A003766 a(9) = 371397240,
%F A003766 a(10) = 2537155684,
%F A003766 a(11) = 17047659916,
%F A003766 a(12) = 113102692016,
%F A003766 a(13) = 742597784164,
%F A003766 a(14) = 4835184613212,
%F A003766 a(15) = 31267479066856,
%F A003766 a(16) = 201066698078244,
%F A003766 a(17) = 1286998671857356 and
%F A003766 a(n) = 14a(n-1) - 41a(n-2) - 193a(n-3) + 1025a(n-4) + 49a(n-5) - 5867a(n-6) 
               + 7519a(n-7) + 6908a(n-8) - 23055a(n-9) + 16228a(n-10) + 2530a(n-11) 
               - 7196a(n-12) + 832a(n-13) + 1568a(n-14) - 608a(n-15) + 64a(n-16).
%Y A003766 Sequence in context: A126679 A165436 A147796 this_sequence A046182 A092122 
               A003460
%Y A003766 Adjacent sequences: A003763 A003764 A003765 this_sequence A003767 A003768 
               A003769
%K A003766 nonn
%O A003766 1,1
%A A003766 Frans Faase (Frans_LiXia(AT)wxs.nl)
%E A003766 Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), 
               Feb 03 2009