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A028469
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Number of perfect matchings in graph P_{7} X P_{2n}.
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4
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21, 781, 31529, 1292697, 53175517, 2188978117, 90124167441, 3710708201969, 152783289861989, 6290652543875133, 259009513044645817, 10664383939345916681, 439092316687230373293, 18079062471131097321077
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| 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.
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LINKS
| 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
| G.f.: (-x^7 + 55*x^6 - 637*x^5 + 2355*x^4 - 3367*x^3 + 1905*x^2 - 395*x + 21)/(x^8 - 56*x^7 + 672*x^6 - 2632*x^5 + 4094*x^4 - 2632*x^3 + 672*x^2 - 56*x + 1).
(Faase:) If b(n) denotes the number of perfect matchings in P_7 X P_n we have:
b(1) = 0,
b(2) = 21,
b(3) = 0,
b(4) = 781,
b(5) = 0,
b(6) = 31529,
b(7) = 0,
b(8) = 1292697,
b(9) = 0,
b(10) = 53175517,
b(11) = 0,
b(12) = 2188978117,
b(13) = 0,
b(14) = 90124167441,
b(15) = 0,
b(16) = 3710708201969, and
b(n) = 56b(n-2) - 672b(n-4) + 2632b(n-6) - 4094b(n-8) + 2632b(n-10) - 672b(n-12) + 56b(n-14) - b(n-16).
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CROSSREFS
| Row 7 of array A099390.
Sequence in context: A062755 A012850 A012645 * A119414 A012819 A202810
Adjacent sequences: A028466 A028467 A028468 * A028470 A028471 A028472
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KEYWORD
| nonn
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AUTHOR
| Per Hakan Lundow (phl(AT)theophys.kth.se)
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EXTENSIONS
| Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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