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
Alois P. Heinz, Table of n, a(n) for n = 0..939
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 23 2007
STATUS
approved