A126765 a(n) = number of L-convex polyominoes inscribed in an (n+1) X (n+1) box.

1, 5, 42, 402, 4070, 42510, 452900, 4891988, 53376966, 586921790, 6493225772, 72192371100, 805935279708, 9028253155628, 101433497725320, 1142504966609512, 12897113121607750, 145870996300613406, 1652690392388658012, 18753389068268792780, 213091273336786301940

Offset: 0

Author

N. J. A. Sloane, Feb 23 2007

Keywords

• nonn

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

• Alois P. Heinz, Table of n, a(n) for n = 0..939

Crossrefs

Cf. A000105, A126764.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 4*n+1, (12*(4*n-1)*(2*n-1)*(n-1)^2*
      a(n-1)-4*(n-2)*(2*n-3)*n*(4*n+1)*a(n-2))/((4*n-3)*(2*n-1)*n*(n-1)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 23 2023

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 *)

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