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A100683
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a(n) = a(n-1) + a(n-2) + a(n-3); a(0) = -1, a(1) = 2, a(2) = 2.
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54
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-1, 2, 2, 3, 7, 12, 22, 41, 75, 138, 254, 467, 859, 1580, 2906, 5345, 9831, 18082, 33258, 61171, 112511, 206940, 380622, 700073, 1287635, 2368330, 4356038, 8012003, 14736371, 27104412, 49852786, 91693569, 168650767, 310197122
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OFFSET
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0,2
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COMMENTS
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A tribonacci sequence.
For n >= 2, a(n+2) is the number of ways to tile this figure of length n with squares, dominoes, and "trominoes" (of length 3):
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|_|_|___________
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As an example, here is one of the 254 possible tilings of this figure of length 8 with squares, dominoes, and trominoes:
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|_|_____|_|___|_|. (End)
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LINKS
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FORMULA
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O.g.f.: -(1-3x-x^2)/(1-x-x^2-x^3). - R. J. Mathar, Aug 22 2008
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MAPLE
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a[0]:=-1:a[1]:=2:a[2]:=2:for n from 3 to 42 do a[n]:=a[n-1]+a[n-2]+a[n-3] od: seq(a[n], n=0..42);
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MATHEMATICA
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a[0] = -1; a[1] = a[2] = 2; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 35}] (* Robert G. Wilson v, Dec 09 2004 *)
LinearRecurrence[{1, 1, 1}, {-1, 2, 2}, 34] (* Ray Chandler, Dec 08 2013 *)
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PROG
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(PARI) Vec(-(1-3*x-x^2)/(1-x-x^2-x^3) + O(x^70)) \\ Michel Marcus, Sep 25 2015
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CROSSREFS
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KEYWORD
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sign,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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