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%I M2924 #38 Aug 22 2021 14:30:55
%S 1,3,12,54,260,1310,6821,36413,198227,1096259,6141764,34784432,
%T 198828308,1145544680,6645621536,38786564126,227585926704,
%U 1341757498470,7944249448686,47217102715624,281615520373954,1684957401786580,10110628493454482,60830401073611514
%N Number of column-convex polyominoes with perimeter n.
%C 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_, Nov 29 2007
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Colin Barker, <a href="/A006026/b006026.txt">Table of n, a(n) for n = 1..1000</a>
%H M.-P. Delest, <a href="/A006026/a006026.pdf">Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos</a>, Ph.D. Dissertation, Université Bordeaux I, May 1987. [Scanned copy, with permission. A very large file.]
%H M.-P. Delest, <a href="/A006026/a006026_1.pdf">Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos</a>, Ph.D. Dissertation, Université Bordeaux I, May 1987. (Annotated scanned copy of a small part of the thesis)
%H M.-P. Delest, <a href="http://dx.doi.org/10.1016/0097-3165(88)90071-4">Generating functions for column-convex polyominoes</a>, J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.
%H Maylis P. Delest and Serge Dulucq, <a href="https://hrcak.srce.hr/137083">Enumeration of Directed Column-Convex Animals with a Given Perimeter and Area</a>, Croatica Chemica Acta, 66 (1993), 59-80.
%H G. S. Joyce and A. J. Guttmann, <a href="http://dx.doi.org/10.1088/0305-4470/27/13/012">Exact results for the generating function of directed column-convex animals on the square lattice</a>, J. Physics A: Math. General 27 (1994) 4359-4367.
%F The g.f. A(x) = x + x^2 + 3x^3 + ... satisfies A^3 - 3A^2 + (1+2x)A - x = 0. - _David Callan_, Nov 29 2007
%t 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_, Nov 29 2007 *)
%Y Cf. A006027, A259332, A259333.
%K nonn,easy
%O 1,2
%A _Simon Plouffe_
%E Delest thesis provided by M.-P. Delest and scanned by _Simon Plouffe_, Jan 16 2016
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