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Search: id:A003757
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| A003757 |
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Number of perfect matchings (or domino tilings) in D_4 X P_(n-1). |
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+0
2
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| 0, 1, 1, 6, 13, 49, 132, 433, 1261, 3942, 11809, 36289, 109824, 335425, 1018849, 3104934, 9443629, 28756657, 87504516, 266383153, 810723277, 2467770054, 7510988353, 22861948801, 69584925696, 211799836801, 644660351425
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Here D_4 is the graph on 4 vertices with edges (1,2), (1,3), (2,3), (1.4): a triangular kite with a tail.
This is a divisibility sequence; that is, if n divides m, then a(n) divides a(m). [From T. D. Noe (noe(AT)sspectra.com), Dec 22 2008]
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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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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. J. Faase, Results from the counting program
F. Faase, Counting Hamilton cycles in product graphs
Paul Raff, Spanning Trees in Grid Graphs
Index entries for sequences related to dominoes
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FORMULA
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a(n) = a(n-1) + 6a(n-2) + a(n-3) - a(n-4), n>4.
G.f.: x(1-x^2)/(1-x-6x^2-x^3+x^4) [From T. D. Noe (noe(AT)sspectra.com), Dec 22 2008]
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MATHEMATICA
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CoefficientList[Series[x(1-x^2)/(1-x-6x^2-x^3+x^4), {x, 0, 30}], x] [From T. D. Noe (noe(AT)sspectra.com), Dec 22 2008]
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CROSSREFS
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Sequence in context: A100905 A041489 A131188 this_sequence A064521 A111366 A119110
Adjacent sequences: A003754 A003755 A003756 this_sequence A003758 A003759 A003760
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KEYWORD
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nonn
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
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Changed offset and name T. D. Noe (noe(AT)sspectra.com), Dec 22 2008
Prepended 0 and 1. - T. D. Noe (noe(AT)sspectra.com), Dec 22 2008
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