cp's OEIS Frontend

A084477 Number of fault-free tilings of a 4 X 3n rectangle with right trominoes.

%I A084477 #19 Mar 28 2017 06:57:30
%S A084477 4,2,8,48,288,1728,10368,62208,373248,2239488,13436928,80621568,
%T A084477 483729408,2902376448,17414258688,104485552128,626913312768,
%U A084477 3761479876608,22568879259648,135413275557888,812479653347328,4874877920083968,29249267520503808
%N A084477 Number of fault-free tilings of a 4 X 3n rectangle with right trominoes.
%C A084477 A tromino is a 3-celled L-shaped piece (a 2 X 2 square with one of the four cells omitted). - _N. J. A. Sloane_, Mar 28 2017
%C A084477 Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A046984(n).
%H A084477 Colin Barker, <a href="/A084477/b084477.txt">Table of n, a(n) for n = 1..1000</a>
%H A084477 M. Aanjaneya and S. P. Pal, <a href="http://arXiv.org/abs/math.CO/0610925">Faultfree tromino tilings of rectangles</a>
%H A084477 C. Moore, <a href="http://arXiv.org/abs/math.CO/9905012">[math/9905012] Some Polyomino Tilings of the Plane</a>
%H A084477 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (6).
%F A084477 a(n) = 2*A067411(n-2) for n>1.
%F A084477 G.f.: 2*z(2-11*z-2*z^2) / (1-6*z).
%F A084477 a(n) = 8 * 6^(n-3) for n>2.
%F A084477 G.f.: 9/2 - x - 1/Q(0) where Q(k)= 1 + 5^k/(1 - 2*x/(2*x + 5^k/Q(k+1) )); (continued fraction ). - _Sergei N. Gladkovskii_, Apr 10 2013
%F A084477 a(n) = 6*a(n-1) for n>2. - _Colin Barker_, Mar 28 2017
%o A084477 (PARI) Vec(2*x*(2 - 11*x - 2*x^2) / (1 - 6*x) + O(x^30)) \\ _Colin Barker_, Mar 28 2017
%Y A084477 Cf. A084478, A084479, A084480, A084481.
%K A084477 nonn,easy
%O A084477 1,1
%A A084477 _Ralf Stephan_, May 27 2003