Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #29 Feb 07 2024 12:55:51
%S 0,1,8,47,264,1480,8305,46616,261663,1468752,8244304,46276385,
%T 259755560,1458042831,8184190168,45938958232,257861540369,
%U 1447411446840,8124514782015,45603992276896,255981331487648
%N Number of Hamiltonian paths from NW to SW corners in a grid with 2n rows and 4 columns.
%H Vincenzo Librandi, <a href="/A014524/b014524.txt">Table of n, a(n) for n = 0..1000</a>
%H K. L. Collins and L. B. Krompart, <a href="http://dx.doi.org/10.1016/0012-365X(95)00330-Y">The number of Hamiltonian paths in a rectangular grid</a>, Discrete Math. 169 (1997), 29-38.
%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-9,7,-1).
%F From _Colin Barker_, May 20 2013: (Start)
%F a(n) = 7*a(n-1)-9*a(n-2)+7*a(n-3)-a(n-4).
%F G.f.: x*(x+1)/(x^4-7*x^3+9*x^2-7*x+1). (End)
%e Illustration of a(1)=1:
%e .__.__.__.
%e .__.__.__|
%e Illustration of a few of the 8 solutions to a(2):
%e .__.__.__. . .__.__. . .__.__. .__.__.__.
%e .__.__. | | | .__| |__| .__| .__.__.__|
%e |__ | | |__| |__. .__. |__. |__.__.__.
%e .__| |__| .__.__.__| | |__.__| .__.__.__|
%t CoefficientList[Series[x (x + 1)/(x^4 - 7 x^3 + 9 x^2 - 7 x + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%Y Even bisection of column 4 of A271592.
%Y Cf. A000532, A181688, A014523, A014585, A003695, A006864.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
%E Name clarified by _Andrew Howroyd_, Apr 10 2016