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Number of directed EG-convex polyominoes on the honeycomb lattice with given semiperimeter.
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%I #18 Oct 29 2023 22:24:43

%S 1,0,3,2,9,12,31,53,116,215,446,849,1726,3320,6688,12932,25925,50297,

%T 100546,195562,390257,760630,1516233,2960502,5897425,11533047,

%U 22964739,44972711,89528901,175546608,349425044,685913758,1365249931,2682660933

%N Number of directed EG-convex polyominoes on the honeycomb lattice with given semiperimeter.

%D Fouad Ibn-Majdoub-Hassani, Combinatoire de polyominos et des tableaux décalés oscillants, Thèse de Doctorat. Laboratoire de Recherche en Informatique, Université Paris-Sud XI, France.

%D Alain Denise, Christoph Durr, and Fouad Ibn-Majdoub-Hassani, Enumération et génération aléatoire de polyominos convexes en réseau 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.

%F G.f.: x^3*((1-2*x)*(-3+x+3*x^2+2*x^3)+(1-x-x^2)*(1-4*x^2)^(1/2))/(2*(1+x)*(1-2*x)*(1-x-x^2)*(-1+x+2*x^2+x^3)).

%t CoefficientList[Series[x^3*((1-2*x)*(-3+x+3*x^2+2*x^3)+(1-x-x^2)*(1-4*x^2)^(1/2))/(2*(1+x)*(1-2*x)*(1-x-x^2)*(-1+x+2*x^2+x^3)),{x,0,36}],x] (* _Stefano Spezia_, Oct 28 2023 *)

%K nonn,easy

%O 3,3

%A _Fouad IBN MAJDOUB HASSANI_, Feb 28 2000

%E More terms from _James A. Sellers_, Mar 01 2000