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A053151
Number of directed EG-convex polyominoes on the honeycomb lattice with given semiperimeter.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Mar 01 2000
STATUS
approved