A006865 Number of Hamiltonian cycles in P_5 X P_{2n}: a(n) = 11*a(n-1) + 2*a(n-3). (Formerly M4946)

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

Harvey P. Dale, Table of n, a(n) for n = 1..960

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 Hamiltonian cycles in product graphs

F. Faase, Results from the counting program

Y. H. H. Kwong, A Matrix Method for Counting Hamiltonian Cycles on Grid Graphs, European J. of Combinatorics 15 (1994), 277-283.

Index entries for linear recurrences with constant coefficients, signature (11,0,2).

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

Adjacent sequences: A006862 A006863 A006864 * A006866 A006867 A006868

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