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A028469 Number of perfect matchings in graph P_{7} X P_{2n}. 6
1, 21, 781, 31529, 1292697, 53175517, 2188978117, 90124167441, 3710708201969, 152783289861989, 6290652543875133, 259009513044645817, 10664383939345916681, 439092316687230373293, 18079062471131097321077 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

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, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], Table 6.

FORMULA

G.f.: (-x^7 +35*x^6 -277*x^5 +727*x^4 -727*x^3 +277*x^2 -35*x +1) / (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).

CROSSREFS

Row 7 of array A099390.

Sequence in context: A012850 A012645 A220069 * A119414 A012819 A202810

Adjacent sequences:  A028466 A028467 A028468 * A028470 A028471 A028472

KEYWORD

nonn

AUTHOR

Per H. Lundow

EXTENSIONS

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

STATUS

approved

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Last modified May 26 05:18 EDT 2017. Contains 287074 sequences.