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Search: id:A028468
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| A028468 |
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Number of perfect matchings in graph P_{6} X P_{n}. |
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+0
4
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| 1, 1, 13, 41, 281, 1183, 6728, 31529, 167089, 817991, 4213133, 21001799, 106912793, 536948224, 2720246633, 13704300553, 69289288909, 349519610713, 1765722581057, 8911652846951, 45005025662792
(list; graph; listen)
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OFFSET
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0,3
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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.
Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
R. P. Stanley, Enumerative Combinatorics I, p. 292.
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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
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
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FORMULA
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a(1) = 1,
a(2) = 13,
a(3) = 41,
a(4) = 281,
a(5) = 1183,
a(6) = 6728,
a(7) = 31529,
a(8) = 167089,
a(9) = 817991,
a(10) = 4213133,
a(11) = 21001799,
a(12) = 106912793,
a(13) = 536948224,
a(14) = 2720246633, and
a(n) = 40a(n-2) - 416a(n-4) + 1224a(n-6) - 1224a(n-8) + 416a(n-10) - 40a(n-12) + a(n-14).
G.f.: (1-8*x^2-2*x^3+8*x^4-x^6)/(1-x-20*x^2-10*x^3+38*x^4+10*x^5-20*x^6+x^7+x^8).
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CROSSREFS
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Row 6 of array A099390.
Sequence in context: A141970 A167240 A147247 this_sequence A146995 A102130 A080186
Adjacent sequences: A028465 A028466 A028467 this_sequence A028469 A028470 A028471
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Per Hakan Lundow (phl(AT)theophys.kth.se)
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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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