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 A084479 Number of fault-free tilings of a 5 X 3n rectangle with right trominoes. 5
 72, 384, 3360, 21504, 163968, 1136640, 8283648, 58791936, 423121920, 3022872576, 21679875072, 155169515520, 1111792499712, 7961492434944, 57028930483200, 408439216748544, 2925470825868288, 20952944438968320, 150073631759459328, 1074876158496638976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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 Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084478(n). LINKS Colin Barker, Table of n, a(n) for n = 2..1000 M. Aanjaneya and S. P. Pal, Faultfree tromino tilings of rectangles, arXiv:math/0610925 [math.CO], 2006. C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999. Index entries for linear recurrences with constant coefficients, signature (2,31,40,20). FORMULA G.f.: 24*z^2*(3 + 10*z + 15*z^2) / (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4). 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 MATHEMATICA LinearRecurrence[{2, 31, 40, 20}, {72, 384, 3360, 21504}, 20] (* Jean-François Alcover, Jan 07 2019 *) PROG (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 CROSSREFS Cf. A084478, A084477, A084480, A084481. Sequence in context: A090788 A192792 A303621 * A084478 A187158 A164377 Adjacent sequences:  A084476 A084477 A084478 * A084480 A084481 A084482 KEYWORD nonn,easy AUTHOR Ralf Stephan, May 27 2003 STATUS approved

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Last modified September 20 06:19 EDT 2019. Contains 327212 sequences. (Running on oeis4.)