A053151 Number of directed EG-convex polyominoes on the honeycomb lattice with given semiperimeter.

1, 0, 3, 2, 9, 12, 31, 53, 116, 215, 446, 849, 1726, 3320, 6688, 12932, 25925, 50297, 100546, 195562, 390257, 760630, 1516233, 2960502, 5897425, 11533047, 22964739, 44972711, 89528901, 175546608, 349425044, 685913758, 1365249931, 2682660933

Offset: 3

Author

Fouad IBN MAJDOUB HASSANI, Feb 28 2000

Keywords

• nonn
• easy

References

• 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.
• 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.

Programs

Mathematica

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 *)

Formula

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)).

Extensions

More terms from James Sellers, Mar 01 2000