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A006865 Number of Hamiltonian cycles in P_5 X P_{2n}: a(n) = 11a(n-1)+2a(n-3).
(Formerly M4946)
4
1, 14, 154, 1696, 18684, 205832, 2267544, 24980352, 275195536, 3031685984, 33398506528, 367933962880, 4053336963648, 44653503613184, 491924407670784, 5419275158305920, 59701333748591488, 657698520049847936, 7245522270864939136, 79820147647011513472 (list; graph; refs; listen; history; text; internal format)
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.

Kwong, Y. H. H.; Enumeration of Hamiltonian cycles in P_4 X P_n and P_5 X P_n. Ars Combin. 33 (1992), 87-96.

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

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 Hamilton cycles in product graphs

F. Faase, Results from the counting program

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

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Last modified November 16 21:45 EST 2018. Contains 317275 sequences. (Running on oeis4.)