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A121580
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Number of cells in column 1 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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1, 3, 11, 53, 317, 2237, 18077, 164237, 1656077, 18348557, 221561357, 2895986957, 40737113357, 613623026957, 9854521894157, 168083120422157, 3034505335078157, 57810369261862157, 1159018646647078157
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A100822(n,k),k=1..n).
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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)=a(n-1)+(n-1)!*([1+n(n-1)/2] for n>=2.
a(n)=(1/2)Sum(j!,j=0..n+1) - n!. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008
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EXAMPLE
| a(2)=3 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 2 and 1 cells in their first columns.
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MAPLE
| a[1]:=1: for n from 2 to 22 do a[n]:=a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n], n=1..22);
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CROSSREFS
| Cf. A100822.
Sequence in context: A074512 A005502 A000255 * A081367 A156171 A129093
Adjacent sequences: A121577 A121578 A121579 * A121581 A121582 A121583
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 09 2006
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