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A121555
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Number of 1-cell columns in 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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1, 2, 7, 32, 178, 1164, 8748, 74304, 704016, 7362720, 84255840, 1047358080, 14054739840, 202514376960, 3118666924800, 51119166873600, 888640952371200, 16330301780889600, 316322420114534400, 6441691128993792000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A121554(n,k),k=0..n).
It appears that a(n) is a function of the harmonic numbers [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 13 2010]
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REFERENCES
| 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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FORMULA
| a(1)=1, a(n)=n*a(n-1)+(n-2)!*(n-2) for n>=2.
a(n)= n!*(h(n)-(n-1)/n), where h(n)=sum(1/k,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 13 2010]
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EXAMPLE
| a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 2 columns with exactly 1 cell.
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MAPLE
| a[1]:=1: for n from 2 to 23 do a[n]:=n*a[n-1]+(n-2)!*(n-2) od: seq(a[n], n=1..23);
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CROSSREFS
| Cf. A121554.
Sequence in context: A059439 A190123 A006014 * A097900 A198891 A000153
Adjacent sequences: A121552 A121553 A121554 * A121556 A121557 A121558
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2006
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