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A084478
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Number of tilings of a 5 X 3n rectangle with right trominoes.
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8
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1, 0, 72, 384, 8544, 76800, 1168512, 12785664, 170678784, 2014648320, 25633231872, 311423852544, 3892030055424, 47803588208640, 593425578949632, 7318730222874624, 90624271197041664, 1119402280975349760, 13847850677651745792, 171150049715628539904
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OFFSET
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0,3
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COMMENTS
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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
There is a sign typo with respect to the g.f. in the paper.
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..900
C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999.
Index entries for linear recurrences with constant coefficients, signature (2,103,280,380).
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FORMULA
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G.f.: (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4) / (1 - 2*z - 103*z^2 - 280*z^3 - 380*z^4).
a(n) = 2*a(n-1) + 103*a(n-2) + 280*a(n-3) + 380*a(n-4) for n > 4. - Colin Barker, Mar 27 2017
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MATHEMATICA
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LinearRecurrence[{2, 103, 280, 380}, {72, 384, 8544, 76800}, 20] (* Jean-François Alcover, Jan 07 2019 *)
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PROG
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(PARI) Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 103*x^2 - 280*x^3 - 380*x^4) + O(x^30)) \\ Colin Barker, Mar 27 2017
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CROSSREFS
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Cf. A084477, A084479, A084480, A084481.
Sequence in context: A192792 A303621 A084479 * A187158 A164377 A156632
Adjacent sequences: A084475 A084476 A084477 * A084479 A084480 A084481
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan, May 27 2003
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EXTENSIONS
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a(0) and a(1) prepended by Alois P. Heinz, Feb 21 2022
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STATUS
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approved
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