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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

%I M4946 #26 Feb 07 2024 09:37:08

%S 1,14,154,1696,18684,205832,2267544,24980352,275195536,3031685984,

%T 33398506528,367933962880,4053336963648,44653503613184,

%U 491924407670784,5419275158305920,59701333748591488,657698520049847936,7245522270864939136,79820147647011513472

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

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

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harvey P. Dale, <a href="/A006865/b006865.txt">Table of n, a(n) for n = 1..960</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

%H F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H Y. H. H. Kwong, <a href="https://doi.org/10.1006/eujc.1994.1031">A Matrix Method for Counting Hamiltonian Cycles on Grid Graphs</a>, European J. of Combinatorics 15 (1994), 277-283.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,0,2).

%F G.f.: x*(1+3*x)/(1-11*x-2*x^3). - _Colin Barker_, Aug 29 2012

%t LinearRecurrence[{11,0,2},{1,14,154},20] (* _Harvey P. Dale_, Aug 21 2013 *)

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, kwong(AT)cs.fredonia.edu (Harris Kwong), _Frans J. Faase_

%E More terms from _Harvey P. Dale_, Aug 21 2013

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)