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%I #12 Jan 01 2019 06:31:05
%S 8,779,99051,13049563,1729423756,229435550806,30443972466433,
%T 4039769151988768,536061241088972481,71133264482944200277,
%U 9439112402375129121841,1252534193959746441955912,166206508635573867359551206,22054969579015463381016539631
%N Number of 2-factors 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 Alois P. Heinz, <a href="/A145415/b145415.txt">Table of n, a(n) for n = 1..470</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: If b(n) denotes the number of 2-factors in P_7 X P_n then we have
%F b(1) = 0,
%F b(2) = 8,
%F b(3) = 0,
%F b(4) = 779,
%F b(5) = 0,
%F b(6) = 99051,
%F b(7) = 0,
%F b(8) = 13049563,
%F b(9) = 0,
%F b(10) = 1729423756,
%F b(11) = 0,
%F b(12) = 229435550806,
%F b(13) = 0,
%F b(14) = 30443972466433,
%F b(15) = 0,
%F b(16) = 4039769151988768,
%F b(17) = 0,
%F b(18) = 536061241088972481, and
%F b(n) = 171b(n-2) - 5496b(n-4) + 56617b(n-6) - 240021b(n-8) + 457923b(n-10)
%F - 420254b(n-12) + 186912b(n-14) - 37569b(n-16) + 2584b(n-18).
%p a:= n-> (Matrix([[4039769151988768, 30443972466433, 229435550806, 1729423756, 13049563, 99051, 779, 8, 14/19]]). Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [171, -5496, 56617, -240021, 457923, -420254, 186912, -37569, 2584][i] else 0 fi)^n)[1, 9]: seq(a(n), n=1..20); # _Alois P. Heinz_, Mar 23 2009
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Feb 03 2009
%E More terms from _Alois P. Heinz_, Mar 23 2009
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