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Search: id:A007808
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| A007808 |
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Number of directed column-convex polyominoes of height n: a(k+1)=(k+1)*a(k)+(a(1)+...+a(k)). |
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10
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| 1, 3, 13, 69, 431, 3103, 25341, 231689, 2345851, 26065011, 315386633, 4128697741, 58145826519, 876660153671, 14089181041141, 240455356435473, 4343224875615731, 82776756452911579, 1660133837750060001
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos dirige's verticalement convexes, Actes du 31e Se'minaire Lotharingien de Combinatoire, Publi. IRMA, Universite' Strasbourg I (1993).
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LINKS
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E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos...
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FORMULA
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a(n) = (n^2*a(n-1)-1)/(n-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 26 2003
a(n)=n!*n*[1-Sum(1/j/(j+1)/(j+1)!, j=1..n-1)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 07 2006
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MAPLE
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a:=n->n!*n*(1-add(1/j/(j+1)/(j+1)!, j=1..n-1)): seq(a(n), n=1..22); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 07 2006
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CROSSREFS
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First differences of A056542.
Sequence in context: A067145 A088714 A088368 this_sequence A104989 A119906 A059726
Adjacent sequences: A007805 A007806 A007807 this_sequence A007809 A007810 A007811
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KEYWORD
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nonn
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AUTHOR
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Paul.Zimmermann(AT)loria.fr
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