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A003696
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Number of spanning trees in P_4 X P_n.
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4
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1, 56, 2415, 100352, 4140081, 170537640, 7022359583, 289143013376, 11905151192865, 490179860527896, 20182531537581071, 830989874753525760, 34214941811800329425, 1408756312731277540744
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OFFSET
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1,2
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COMMENTS
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Also number of domino tilings of the 7 X (2n-1) rectangle with upper left corner removed. - Alois P. Heinz, Apr 14 2011
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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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T. D. Noe, Table of n, a(n) for n = 1..200
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
F. Faase, Counting Hamilton cycles in product graphs
P. Raff, Spanning Trees in Grid Graphs. [From Paul Raff, Mar 06 2009]
P. Raff, Analysis of the Number of Spanning Trees of P_4 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff, Mar 06 2009]
Index entries for sequences related to trees
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FORMULA
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a(1) = 1,
a(2) = 56,
a(3) = 2415,
a(4) = 100352,
a(5) = 4140081,
a(6) = 170537640,
a(7) = 7022359583,
a(8) = 289143013376 and
a(n) = 56a(n-1) - 672a(n-2) + 2632a(n-3) - 4094a(n-4) + 2632a(n-5) - 672a(n-6) + 56a(n-7) - a(n-8).
G.f.: x(x^6-49x^4+112x^3-49x^2+1) / (x^8-56x^7 +672x^6-2632x^5 +4094x^4 -2632x^3 +672x^2-56x+1). [From Paul Raff, Mar 06 2009]
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CROSSREFS
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A row of A116469. - N. J. A. Sloane, May 27 2012
Bisection of A189004. - Alois P. Heinz, Sep 20 2012
Sequence in context: A221398 A124101 A198948 * A199709 A205227 A224176
Adjacent sequences: A003693 A003694 A003695 * A003697 A003698 A003699
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KEYWORD
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nonn
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AUTHOR
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Frans J. Faase
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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
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STATUS
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approved
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