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A140710
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Number of maximal initial consecutive columns ending at the same level, summed over 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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1
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1, 3, 10, 38, 172, 944, 6208, 47696, 417952, 4101824, 44491648, 528068096, 6804155392, 94559581184, 1409615239168, 22434345998336, 379633330204672, 6805952938041344, 128854632579186688, 2568966172926181376
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OFFSET
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1,2
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COMMENTS
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a(n)=Sum(k*A140709(n,k),k=1..n).
(1 + x + 2x^2 + 4x^3 + 8x^4 + ...)*(1 + 2x + 6x^2 + 24x^3 + 120^4 + ...) = (1 + 3x + 10x^2 + 38x^3 + 172x^4 + ...). - Gary W. Adamson, Feb 24 2012
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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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Table of n, a(n) for n=1..20.
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FORMULA
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a(n)=2^(n-1)*[1+sum(j^2*(j-1)!/2^j,j=1..n-1)] (n>=1). Rec. rel.: a(n)=(n-1)!(n-1) + 2a(n-1); a(1)=1.
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EXAMPLE
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a(3)=10 because the 6 deco polyominoes of height 3 have columns ending at levels 3, 22, 12, 111, 22, 122, respectively and 1+2+1+3+2+1=10.
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MAPLE
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a:=proc(n) options operator, arrow: 2^(n-1)*(1+sum(j^2*factorial(j-1)/2^j, j= 1..n-1)) end proc: seq(a(n), n=1..20);
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CROSSREFS
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Cf. A140709.
Sequence in context: A074527 A186367 A010842 * A103296 A111749 A149048
Adjacent sequences: A140707 A140708 A140709 * A140711 A140712 A140713
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Jun 03 2008
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STATUS
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approved
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