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%I #9 Apr 08 2020 16:55:30
%S 1,92,5320,301384,17066492,966656134,54756073582,3101696069920,
%T 175698206778318,9952578156814524,563772503196695338,
%U 31935387285412942410,1809007988782552388490,102472842263117124008066,5804663918990466729365476,328810272735298761062754308
%N Number of Hamiltonian cycles in P_7 X P_2n.
%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H Seiichi Manyama, <a href="/A145416/b145416.txt">Table of n, a(n) for n = 1..500</a>
%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 Recurrence:
%F a(1) = 1,
%F a(2) = 92,
%F a(3) = 5320,
%F a(4) = 301384,
%F a(5) = 17066492,
%F a(6) = 966656134,
%F a(7) = 54756073582,
%F a(8) = 3101696069920,
%F a(9) = 175698206778318,
%F a(10) = 9952578156814524,
%F a(11) = 563772503196695338,
%F a(12) = 31935387285412942410,
%F a(13) = 1809007988782552388490,
%F a(14) = 102472842263117124008066,
%F a(15) = 5804663918990466729365476,
%F a(16) = 328810272735298761062754308,
%F a(17) = 18625745945872429428768223714,
%F a(18) = 1055071695766249759732087999456, and
%F a(n) = 85a(n-1) - 1932a(n-2) + 20403a(n-3) - 116734a(n-4) + 386724a(n-5)
%F - 815141a(n-6) + 1251439a(n-7) - 1690670a(n-8) + 2681994a(n-9)
%F - 4008954a(n-10) + 3390877a(n-11) - 1036420a(n-12) - 178842a(n-13)
%F + 92790a(n-14) + 17732a(n-15) - 5972a(n-16) + 1728a(n-17) + 144a(n-18).
%Y Cf. A321172.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 03 2009
%E Recurrence corrected by _Frans J. Faase_, Feb 04 2009
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