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A134437
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Number of cells in the 2nd rows of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
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2
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0, 1, 7, 45, 312, 2400, 20520, 194040, 2016000, 22861440, 281232000, 3732220800, 53169177600, 809512704000, 13120332825600, 225573828480000, 4100866818048000, 78606921609216000
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OFFSET
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1,3
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COMMENTS
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a(n)=Sum(k*A134436(n,k),k=0..n-1).
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REFERENCES
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E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..400
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FORMULA
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a(n)=(1/4)(3n-2)(n-1)(n-1)! Rec. rel.: a(n)=(1/2)(3n-4)(n-1)! + (n-1)a(n-1); a(1)=0.
a(n)=(n+2)!*sum((2*k-1)/(k*(k+1)*(k+2)),k=1..n).[From Gary Detlefs, Sep 20 2011]
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EXAMPLE
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a(2)=1 because the horizontal domino has no cells in the 2nd row and the vertical domino has 1 cell in the 2nd row.
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MAPLE
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seq((1/4)*(3*n-2)*(n-1)*factorial(n-1), n = 1 .. 18)
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MATHEMATICA
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Table[((3n-2)(n-1)(n-1)!)/4, {n, 20}] (* From Harvey P. Dale, Sep 23 2011 *)
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PROG
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(MAGMA)[(3*n-2)*(n-1)*Factorial(n-1)/4: n in [1..20]]; // Vincenzo Librandi, Sep 24 2011
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CROSSREFS
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Cf. A134436.
Sequence in context: A219020 A143835 A103719 * A018927 A001266 A071971
Adjacent sequences: A134434 A134435 A134436 * A134438 A134439 A134440
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Nov 30 2007
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STATUS
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approved
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