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

3,3

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.

Links

Table of n, a(n) for n=3..36.

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)).

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 *)

Crossrefs

Sequence in context: A274827 A038220 A303901 * A053088 A077898 A303631

Adjacent sequences: A053148 A053149 A053150 * A053152 A053153 A053154

Keyword

nonn,easy

Author

Fouad IBN MAJDOUB HASSANI, Feb 28 2000

Extensions

More terms from James A. Sellers, Mar 01 2000

Status

approved