cp's OEIS Frontend

A003729 Number of perfect matchings (or domino tilings) in graph C_{5} X P_{2n}.

%I A003729 #23 Jan 01 2019 06:31:05
%S A003729 11,176,2911,48301,801701,13307111,220880176,3666315811,60855946601,
%T A003729 1010127453401,16766766924211,278305942640176,4619507031938711,
%U A003729 76677648402694901,1272746577484955101,21125893715367851311
%N A003729 Number of perfect matchings (or domino tilings) in graph C_{5} X P_{2n}.
%D A003729 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%D A003729 Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
%H A003729 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 A003729 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003729 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A003729 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.
%H A003729 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%H A003729 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (19, -41, 19, -1).
%F A003729 a(n) = 19a(n-1) - 41a(n-2) + 19a(n-3) - a(n-4), n>4.
%F A003729 G.f. x*(11-33*x+18*x^2-x^3)/(1-19*x+41*x^2-19*x^3+x^4) . [From _R. J. Mathar_, Mar 11 2010]
%t A003729 Rest[CoefficientList[Series[x (11-33x+18x^2-x^3)/(1-19x+41x^2- 19x^3+ x^4), {x,0,20}],x]] (* or *) LinearRecurrence[{19,-41,19,-1},{11,176,2911,48301},20] (* _Harvey P. Dale_, Jul 16 2011 *)
%K A003729 nonn,easy
%O A003729 1,1
%A A003729 _Frans J. Faase_