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A126765 a(n) = number of L-convex polyominoes inscribed in an (n+1) X (n+1) box. 2
1, 5, 42, 402, 4070, 42510, 452900, 4891988, 53376966, 586921790, 6493225772, 72192371100, 805935279708, 9028253155628, 101433497725320, 1142504966609512, 12897113121607750, 145870996300613406, 1652690392388658012, 18753389068268792780, 213091273336786301940 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A126764 for definition of L-convex.

REFERENCES

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: (1/2) * sqrt( (2+5*x-2*x^2+(2-x)*sqrt(1-12*x+4*x^2) )/ (1-12*x+4*x^2) ).

a(n) ~ 2^(n-9/4) * (3+2*sqrt(2))^(n+1) / sqrt((1+sqrt(2))*Pi*n). - Vaclav Kotesovec, Feb 16 2015

MATHEMATICA

CoefficientList[Series[(1/2)Sqrt[(2+5x-2x^2+(2-x)Sqrt[1-12x+4x^2])/ (1-12x+4x^2)], {x, 0, 20}], x] (* Harvey P. Dale, Jun 14 2011 *)

CROSSREFS

Cf. A000105, A126764.

Sequence in context: A241780 A215785 A082145 * A228793 A024492 A217805

Adjacent sequences:  A126762 A126763 A126764 * A126766 A126767 A126768

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 23 2007

STATUS

approved

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Last modified October 20 23:39 EDT 2018. Contains 316405 sequences. (Running on oeis4.)