%I A006026 M2924
%S A006026 1,3,12,54,260,1310,6821,36413
%N A006026 Number of column-convex polyominoes with perimeter n.
%C A006026 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
%D A006026 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006026 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.
%D A006026 Delest, M.-P., Generating functions for column-convex polyominoes. J. 
               Combin. Theory Ser. A 48 (1988), no. 1, 12-31.
%D A006026 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.
%F A006026 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
%t A006026 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
%Y A006026 Sequence in context: A055835 A125188 A054666 this_sequence A158826 A107264 
               A052673
%Y A006026 Adjacent sequences: A006023 A006024 A006025 this_sequence A006027 A006028 
               A006029
%K A006026 nonn
%O A006026 1,2
%A A006026 Simon Plouffe (simon.plouffe(AT)gmail.com)