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A121636
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Number of 2-cell columns starting at level 0 in all of 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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0, 1, 5, 23, 122, 754, 5364, 43308, 391824, 3929616, 43287840, 519711840, 6755460480, 94527008640, 1416783432960, 22646604153600, 384576130713600, 6914404440115200, 131217341055897600, 2621176954176614400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=Sum(k*A121634(n,k), k=0..n-1).
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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)=0, a(2)=1, a(n)=n(n-2)! + (n-1)a(n-1) for n >=3.
a(n)=(n-1)!(n^2-2n-1)/n +(n-1)!(1/1+1/2+...+1/n) (n>=2). [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 22 2008]
a(n)= (n-1)!*(h(n-1)+ n - 2), n>1, where h(n)= sum(1/k,k=1..n) [From Gary Detlefs (getlefs(AT)aol.com), Oct 24 2010]
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EXAMPLE
| a(2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes and only the vertical one has one 2-cell column starting at level 0.
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MAPLE
| a[1]:=0: a[2]:=1: for n from 3 to 23 do a[n]:=n*(n-2)!+(n-1)*a[n-1] od: seq(a[n], n=1..23);
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CROSSREFS
| Cf. A121634, A000142.
Sequence in context: A162815 A033312 A151881 * A200028 A020032 A186755
Adjacent sequences: A121633 A121634 A121635 * A121637 A121638 A121639
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 13 2006
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