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A084479 Number of fault-free tilings of a 5 X 3n rectangle with right trominoes. 5

%I

%S 72,384,3360,21504,163968,1136640,8283648,58791936,423121920,

%T 3022872576,21679875072,155169515520,1111792499712,7961492434944,

%U 57028930483200,408439216748544,2925470825868288,20952944438968320,150073631759459328,1074876158496638976

%N Number of fault-free tilings of a 5 X 3n rectangle with right trominoes.

%C 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 Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084478(n).

%H Colin Barker, <a href="/A084479/b084479.txt">Table of n, a(n) for n = 2..1000</a>

%H M. Aanjaneya and S. P. Pal, <a href="https://arxiv.org/abs/math/0610925">Faultfree tromino tilings of rectangles</a>, arXiv:math/0610925 [math.CO], 2006.

%H C. Moore, <a href="https://arxiv.org/abs/math/9905012">Some Polyomino Tilings of the Plane</a>, arXiv:math/9905012 [math.CO], 1999.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,31,40,20).

%F G.f.: 24*z^2*(3 + 10*z + 15*z^2) / (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4).

%F a(n) = 2*a(n-1) + 31*a(n-2) + 40*a(n-3) + 20*a(n-4) for n > 5. - _Colin Barker_, Mar 28 2017

%t LinearRecurrence[{2, 31, 40, 20}, {72, 384, 3360, 21504}, 20] (* _Jean-Fran├žois Alcover_, Jan 07 2019 *)

%o (PARI) Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 31*x^2 - 40*x^3 - 20*x^4) + O(x^30)) \\ _Colin Barker_, Mar 28 2017

%Y Cf. A084478, A084477, A084480, A084481.

%K nonn,easy

%O 2,1

%A _Ralf Stephan_, May 27 2003

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)