%I #14 Jan 01 2019 06:31:05
%S 2,40,240,1558,8300,43438,212700,1014700,4691580,21257258,94520524,
%T 414149254,1791339472,7664373014,32481662616,136520499746,
%U 569599125312,2361080470268,9730117780704,39888323454064
%N Number of Hamiltonian paths in D_4 X P_n.
%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H 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 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%F a(1) = 2,
%F a(2) = 40,
%F a(3) = 240,
%F a(4) = 1558,
%F a(5) = 8300,
%F a(6) = 43438,
%F a(7) = 212700,
%F a(8) = 1014700,
%F a(9) = 4691580,
%F a(10) = 21257258,
%F a(11) = 94520524,
%F a(12) = 414149254,
%F a(13) = 1791339472,
%F a(14) = 7664373014,
%F a(15) = 32481662616,
%F a(16) = 136520499746,
%F a(17) = 569599125312,
%F a(18) = 2361080470268 and
%F a(n) = 11a(n-1) - 34a(n-2) - 22a(n-3) + 266a(n-4) - 270a(n-5) - 454a(n-6) + 986a(n-7) - 247a(n-8) - 887a(n-9) + 1013a(n-10) - 259a(n-11) - 353a(n-12) + 417a(n-13) - 225a(n-14) + 71a(n-15) - 13a(n-16) + a(n-17).
%K nonn
%O 1,1
%A _Frans J. Faase_
%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009
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