1,1

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.

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.

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).

Row 7 of array A099390.

Sequence in context: A062755 A012850 A012645 this_sequence A119414 A012819 A041843

Adjacent sequences: A028466 A028467 A028468 this_sequence A028470 A028471 A028472

nonn

Per Hakan Lundow (phl(AT)theophys.kth.se)

Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009