0,2

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

R. P. Stanley, Enumerative Combinatorics I, p. 292.

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. Faase, Counting Hamilton cycles in product graphs

James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2

Index entries for sequences related to dominoes

If b(n) denotes the number of perfect matchings (or domino tilings) in P_5 X P_n we have:

b(1) = 0,

b(2) = 8,

b(3) = 0,

b(4) = 95,

b(5) = 0,

b(6) = 1183,

b(7) = 0,

b(8) = 14824 and

b(n) = 15b(n-2) - 32b(n-4) + 15b(n-6) - b(n-8).

G.f.: (1-7*x+7*x^2-x^3)/(1-15*x+32*x^2-15*x^3+x^4).

Let M be the 4 X 4 matrix |1 0 2 8 | 0 1 0 2 | 2 1 5 21| 1 1 1 8 |; then a(n) = M^n(4, 4). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 08, 2003

Lim_{n -> Inf} a(n)/a(n-1) = (3 + Sqrt(5))*(5 + Sqrt(21))/4 = 12.54375443458... - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 13 = 2005.

Row 5 of array A099390.

Sequence in context: A010565 A080208 A099298 this_sequence A121785 A116144 A074114

Adjacent sequences: A003772 A003773 A003774 this_sequence A003776 A003777 A003778

nonn

Frans Faase (Frans_LiXia(AT)wxs.nl)

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