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A006865
Number of Hamiltonian cycles in P_5 X P_{2n}: a(n) = 11*a(n-1) + 2*a(n-3).
(Formerly M4946)
5
1, 14, 154, 1696, 18684, 205832, 2267544, 24980352, 275195536, 3031685984, 33398506528, 367933962880, 4053336963648, 44653503613184, 491924407670784, 5419275158305920, 59701333748591488, 657698520049847936, 7245522270864939136, 79820147647011513472
OFFSET
1,2
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
Y. H. H. Kwong, Enumeration of Hamiltonian cycles in P_4 X P_n and P_5 X P_n. Ars Combin. 33 (1992), 87-96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
Y. H. H. Kwong, A Matrix Method for Counting Hamiltonian Cycles on Grid Graphs, European J. of Combinatorics 15 (1994), 277-283.
FORMULA
G.f.: x*(1+3*x)/(1-11*x-2*x^3). - Colin Barker, Aug 29 2012
MATHEMATICA
LinearRecurrence[{11, 0, 2}, {1, 14, 154}, 20] (* Harvey P. Dale, Aug 21 2013 *)
CROSSREFS
Sequence in context: A125426 A004986 A154248 * A263474 A154347 A001707
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, kwong(AT)cs.fredonia.edu (Harris Kwong), Frans J. Faase
EXTENSIONS
More terms from Harvey P. Dale, Aug 21 2013
STATUS
approved