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A121639
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Number of 2-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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1
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0, 1, 5, 25, 147, 996, 7668, 66264, 635976, 6717600, 77482080, 969338880, 13076778240, 189261999360, 2925629280000, 48111515827200, 838731380659200, 15451544605593600, 299960798422118400, 6120505381423104000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=Sum(k*A121637(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(3)=5, a(n)=na(n-1)+(n-1)!-(n-3)! for n>=4.
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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.
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MAPLE
| a[1]:=0: a[2]:=1: a[3]:=5: for n from 4 to 43 do a[n]:=n*a[n-1]+(n-1)!-(n-3)! od: seq(a[n], n=1..23);
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CROSSREFS
| Cf. A121637, A121555.
Sequence in context: A114870 A199319 A049427 * A098349 A098212 A002050
Adjacent sequences: A121636 A121637 A121638 * A121640 A121641 A121642
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 14 2006
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