|
%I #15 Apr 21 2023 13:37:15
%S 8,137,2016,30521,459544,6926545,104379840,1573019185,23705440040,
%T 357242140889,5383654944672,81131924020457,1222661758446136,
%U 18425567948435617,277674141464763264,4184561857758579553,63061536262455564872,950340200711850811433
%N Number of perfect matchings (or domino tilings) in O_6 X P_n.
%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,47,-8,-47,12,1).
%F For n>6, a(n) = 12*a(n-1) + 47*a(n-2) - 8*a(n-3) - 47*a(n-4) + 12*a(n-5) + a(n-6).
%F G.f.: -x*(x^5 +12*x^4 -46*x^3 -4*x^2 +41*x +8)/(x^6 +12*x^5 -47*x^4 -8*x^3 +47*x^2 +12*x -1). [_Colin Barker_, Aug 23 2012]
%t CoefficientList[Series[-(x^5 + 12*x^4 - 46*x^3 - 4*x^2 + 41*x + 8)/(x^6 + 12*x^5 - 47*x^4 - 8*x^3 + 47*x^2 + 12*x - 1), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Sep 03 2022 *)
%t LinearRecurrence[{12,47,-8,-47,12,1},{8,137,2016,30521,459544,6926545},20] (* _Harvey P. Dale_, Apr 21 2023 *)
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Feb 03 2009
%E More terms from _Max Alekseyev_, Jun 24 2011
|
