3,3

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.

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.

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.

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)

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(AT)math.ucdavis.edu), Oct 26 2005)

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)

Sequence in context: A064367 A113980 A095675 this_sequence A091811 A075856 A025520

Adjacent sequences: A006740 A006741 A006742 this_sequence A006744 A006745 A006746

nonn,easy,nice

Simon Plouffe (plouffe(AT)math.uqam.ca), njas

Additional references from Fouad IBN MAJDOUB HASSANI (Fouad.Hassani(AT)genset.fr), Feb 28 2000.