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A145415
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Number of 2-factors in P_7 X P_2n.
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0
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8, 779, 99051, 13049563, 1729423756, 229435550806, 30443972466433, 4039769151988768, 536061241088972481, 71133264482944200277, 9439112402375129121841, 1252534193959746441955912, 166206508635573867359551206, 22054969579015463381016539631
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OFFSET
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1,1
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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Table of n, a(n) for n=1..14.
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, Counting Hamilton cycles in product graphs.
F. Faase, Results from the counting program
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FORMULA
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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).
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MAPLE
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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
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CROSSREFS
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Sequence in context: A181153 A184974 A060183 * A204464 A001547 A168310
Adjacent sequences: A145412 A145413 A145414 * A145416 A145417 A145418
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Feb 03 2009
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EXTENSIONS
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More terms from Alois P. Heinz, Mar 23 2009
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STATUS
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approved
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