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 A145415 Number of 2-factors in P_7 X P_2n. 2
 8, 779, 99051, 13049563, 1729423756, 229435550806, 30443972466433, 4039769151988768, 536061241088972481, 71133264482944200277, 9439112402375129121841, 1252534193959746441955912, 166206508635573867359551206, 22054969579015463381016539631 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..470 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154. F. Faase, Results from the counting program FORMULA Recurrence: If b(n) denotes the number of 2-factors in P_7 X P_n then we have b(1) = 0, b(2) = 8, b(3) = 0, b(4) = 779, b(5) = 0, b(6) = 99051, b(7) = 0, b(8) = 13049563, b(9) = 0, b(10) = 1729423756, b(11) = 0, b(12) = 229435550806, b(13) = 0, b(14) = 30443972466433, b(15) = 0, b(16) = 4039769151988768, b(17) = 0, b(18) = 536061241088972481, and b(n) = 171b(n-2) - 5496b(n-4) + 56617b(n-6) - 240021b(n-8) + 457923b(n-10) - 420254b(n-12) + 186912b(n-14) - 37569b(n-16) + 2584b(n-18). MAPLE 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 CROSSREFS Sequence in context: A060183 A262353 A268148 * A260032 A204464 A001547 Adjacent sequences:  A145412 A145413 A145414 * A145416 A145417 A145418 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 03 2009 EXTENSIONS More terms from Alois P. Heinz, Mar 23 2009 STATUS approved

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)