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

1, 14, 154, 1696, 18684, 205832, 2267544, 24980352, 275195536, 3031685984, 33398506528, 367933962880, 4053336963648, 44653503613184, 491924407670784, 5419275158305920, 59701333748591488, 657698520049847936, 7245522270864939136, 79820147647011513472

Offset: 1

Author

N. J. A. Sloane, kwong(AT)cs.fredonia.edu (Harris Kwong), Frans J. Faase

Keywords

• nonn
• easy

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).

Programs

Mathematica

LinearRecurrence[{11,0,2},{1,14,154},20] (* Harvey P. Dale, Aug 21 2013 *)

Formula

G.f.: x*(1+3*x)/(1-11*x-2*x^3). - Colin Barker, Aug 29 2012

Extensions

More terms from Harvey P. Dale, Aug 21 2013