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A084477
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Number of fault-free tilings of a 4 X 3n rectangle with right trominoes.
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8
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4, 2, 8, 48, 288, 1728, 10368, 62208, 373248, 2239488, 13436928, 80621568, 483729408, 2902376448, 17414258688, 104485552128, 626913312768, 3761479876608, 22568879259648, 135413275557888, 812479653347328, 4874877920083968, 29249267520503808
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OFFSET
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1,1
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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
Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A046984(n).
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LINKS
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FORMULA
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G.f.: 2*z(2-11*z-2*z^2) / (1-6*z).
a(n) = 8 * 6^(n-3) for n>2.
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
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PROG
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(PARI) Vec(2*x*(2 - 11*x - 2*x^2) / (1 - 6*x) + O(x^30)) \\ Colin Barker, Mar 28 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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