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Number of directed column-convex polyominoes with perimeter 2n+2.
(Formerly M1647)
6

%I M1647 #44 Feb 09 2021 06:39:53

%S 1,1,2,6,20,71,263,1005,3933,15684,63505,260390,1079019,4511700,

%T 19011521,80653480,344193353,1476589475,6364258163,27545933212,

%U 119676949397,521739175908,2281673067934,10006784399183,44002280467770,193957104163645,856853526774173

%N Number of directed column-convex polyominoes with perimeter 2n+2.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A006027/b006027.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 M.-P. Delest and S. Dulucq, <a href="https://hrcak.srce.hr/137083?lang=en">Enumeration of directed column-convex animals with given perimeter and area</a>, Croat. Chem. Acta. 66 (1993), 59-80.

%H E. Duchi and S. Rinaldi, <a href="http://dx.doi.org/10.1007/s00026-004-0202-x">An object grammar for column-convex polyominoes</a>, Annals of Combinatorics, 8 (2004), 27-36.

%H S. Dulucq, <a href="/A005819/a005819.pdf">Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots</a>, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)

%F G.f. A(x) = a(1)x^2 + a(2)x^3 + a(3)x^4 + ... satisfies the functional equation A^3 + 2(x-1)A^2 + (2x-1)(x-1)A + (x^2)(x-1) = 0. - D. G. Rogers, May 22 2005

%t m = 30; A[_] = 0;

%t Do[A[x_] = (2(1-x) A[x]^2 - A[x]^3 + x^2 - x^3)/((1-x)(1-2x))+O[x]^m, {m}];

%t CoefficientList[1 + A[x]/x, x] (* _Jean-François Alcover_, Oct 05 2019 *)

%Y Cf. A005435.

%K nonn

%O 1,3

%A _Simon Plouffe_

%E More terms from D. G. Rogers and _Emanuele Munarini_, May 15 2005