Search: id:A006743
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%I A006743 M2255
%S A006743 1,0,3,2,10,14,40,74,176,358,798,1670,3626,7638,16366,34462,
%T A006743 73230,153830,324896,680514,1430336,2987310,6253712,13025954,
%U A006743 27176052,56465878,117458820,243507250,505239264,1045301486
%N A006743 Number of convex polygons of length 2n on honeycomb, or EG-convex polyominoes.
%D A006743 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006743 Alain Denise, Christoph Durr and Fouad Ibn-Majdoub-Hassani. Enumeration 
               et generation aleatoire de polyominos convexes en reseau hexagonal 
               (French) [enumeration and random generation of convex polyominoes 
               in the honeycomb lattice] . In Proceedings of 9th Conference on Formal 
               Power Series and Algebraic Combinatorics, pages 222-234, 1997.
%D A006743 A. J. Guttmann and I. G. Enting, The number of convex polygons on the 
               square and honeycomb lattices, J. Phys. A 21 (1988), L467-L474.
%D A006743 Fouad Ibn-Majdoub-Hassani, Combinatoire de polyominos et des tableaux 
               decales oscillants, These de Doctorat, Laboratoire de Recherche en 
               Informatique, Universite Paris-Sud XI, France.
%F A006743 G.f.: (1-2*x+x^2-x^4-x^2*sqrt(1-4*x^2))/((1+x)^2*(1-2*x)^2), from Paul.Zimmermann(AT)loria.fr 
               (Paul Zimmermann)
%F A006743 For n>=10, (n-5) a(n) = (2n-10) a(n-1) + (7n-47) a(n-2) + (84-12n) a(n-3) 
               + (116-16n) a(n-4) + (16n-128) a(n-5) + (16n-128) a(n-6). This follows 
               from the differential equation (2-2x-12x^2+12x^3+4x^4+16x^6) g(x) 
               + (-x+2x^2+7x^3-12x^4-16x^5+16x^6+16x^7) g'(x) = 2-2x-12x^2+16x^3-2x^4-4x^6 
               satisfied by the g.f. sum_n>=0 a(n+3) x^n = (1-2x+x^2-x^4-x^2 sqrt(1-4x^2))/
               ((1+x)^2 (1-2x)^2). (from Dean Hickerson (dean.hickerson(AT)yahoo.com), 
               Oct 26 2005)
%t A006743 CoefficientList[ Series[(1 - 2x + x^2 - x^4 - x^2*Sqrt[1 - 4*x^2])/(1 
               + x)^2/(1 - 2*x)^2, {x, 0, 29}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Oct 15 2005)
%Y A006743 Sequence in context: A064367 A113980 A095675 this_sequence A091811 A075856 
               A025520
%Y A006743 Adjacent sequences: A006740 A006741 A006742 this_sequence A006744 A006745 
               A006746
%K A006743 nonn,easy,nice
%O A006743 3,3
%A A006743 Simon Plouffe (simon.plouffe(AT)gmail.com), N. J. A. Sloane (njas(AT)research.att.com).
%E A006743 Additional references from Fouad IBN MAJDOUB HASSANI (Fouad.Hassani(AT)genset.fr), 
               Feb 28 2000.

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