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A121553
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Total area 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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1
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1, 4, 20, 122, 874, 7164, 65988, 674064, 7558416, 92276640, 1218255840, 17293495680, 262656570240, 4250077896960, 72992067321600, 1326101675673600, 25410150701107200, 512158576546713600, 10832221231772774400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A121552(n,k), k=n..1+n(n-1)/2).
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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-1)!*[1+n(n-1)/2] for n>=2 (see Barcucci et al. reference, p. 34).
a(n)=n![n(n-1)/4 + 1/1 + 1/2 + ... +1/n]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008
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MAPLE
| a[1]:=1: for n from 2 to 22 do a[n]:=n*a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n], n=1..22);
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CROSSREFS
| Cf. A121552.
Sequence in context: A020028 A020118 A009351 * A067116 A067121 A002793
Adjacent sequences: A121550 A121551 A121552 * A121554 A121555 A121556
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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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