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A285361
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The number of tight 3 X n pavings.
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8
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0, 1, 11, 64, 282, 1071, 3729, 12310, 39296, 122773, 378279, 1154988, 3505542, 10598107, 31957661, 96200098, 289255020, 869075073, 2609845875, 7834779640, 23514823730, 70565441671, 211738266921, 635298685614, 1906063827672, 5718527025901, 17156252164799, 51470098670020
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OFFSET
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0,3
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COMMENTS
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Also, zero together with the third row of the square array A285357.
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LINKS
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D. E. Knuth (Proposer), Problem 12005, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755. For solution see op. cit., 126 (No. 7, 2019), 660-664.
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FORMULA
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a(n) = (1/4) * (3^(n+3) - 5*2^(n+4) + 4*n^2 + 26*n + 53). - Hugo Pfoertner, Mar 14 2018
G.f.: (x+3*x^2)/((1-x)^3*(1-2*x)*(1-3*x)). - Robert Israel, Mar 15 2018
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EXAMPLE
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For n=2 the 11 solutions are 12|32|44, 12|13|44, 12|33|44, 11|22|34, 11|23|43, 12|13|43, 12|32|42, 12|13|14, 12|32|34, 11|23|24, 11|23|44.
(Use the "interactive illustration" link in A285357 (with n=3!) for a graphic display.)
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MAPLE
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seq((1/4) * (3^(n+3) - 5*2^(n+4) + 4*n^2 + 26*n + 53), n=0..50); # Robert Israel, Mar 15 2018
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MATHEMATICA
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LinearRecurrence[{8, -24, 34, -23, 6}, {0, 1, 11, 64, 282}, 30] (* Vincenzo Librandi, Mar 16 2018 *)
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PROG
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(Magma) [(1/4)*(3^(n+3)-5*2^(n+4)+4*n^2+26*n+53): n in [0..30]]; // Vincenzo Librandi, Mar 16 2018
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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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EXTENSIONS
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STATUS
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approved
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