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A006026
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Number of column-convex polyominoes with perimeter n.
(Formerly M2924)
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0
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OFFSET
| 1,2
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COMMENTS
| With offset 2, a(n) = number of directed column-convex polyominoes with directed-site perimeter = n. Directed means every cell (unit square) is reachable from the lower left cell, which is assumed to touch the origin. The directed-site perimeter is the number of unit squares in the first quadrant outside the polyomino but sharing at least one side with it. For example, the polyomino consisting of only one cell (with vertices (0,0),(1,0),(1,1),(0,1)) has directed-site perimeter = 2 due to the squares just above and to the right of it. - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007
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REFERENCES
| M.-P. Delest, Utilisation des Langages Alg\'{e}briques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos. Ph.D. Dissertation, Universit\'{e} Bordeaux I, May 1987.
Delest, M.-P., Generating functions for column-convex polyominoes. J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.
G. S. Joyce and A. J. Guttmann, Exact results for the generating function of directed column-convex animals on the square lattice, J. Physics A: Math. General 27 (1994) 4359-4367.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| The GF A(x)=x+x^2+3x^3+... satisfies A^3 - 3A^2 + (1+2x)A - x = 0. - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007
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MATHEMATICA
| a[1]=1; a[2]=1; a[3]=3; a[n_]/; n>=4 := a[n] = ( 2(n-1)(21n-34)a[n-1] - (3n-8)(23n-43)a[n-2] + 16(n-3)(2n-7)a[n-3] )/(5(n-1)n); Table[a[n], {n, 10}] - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007
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CROSSREFS
| Sequence in context: A055835 A125188 A054666 * A158826 A107264 A200740
Adjacent sequences: A006023 A006024 A006025 * A006027 A006028 A006029
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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