|
%I #18 Jan 23 2023 20:48:14
%S 1,5,42,402,4070,42510,452900,4891988,53376966,586921790,6493225772,
%T 72192371100,805935279708,9028253155628,101433497725320,
%U 1142504966609512,12897113121607750,145870996300613406,1652690392388658012,18753389068268792780,213091273336786301940
%N a(n) = number of L-convex polyominoes inscribed in an (n+1) X (n+1) box.
%C See A126764 for definition of L-convex.
%D 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.
%H Alois P. Heinz, <a href="/A126765/b126765.txt">Table of n, a(n) for n = 0..939</a>
%F 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) ).
%F a(n) ~ 2^(n-9/4) * (3+2*sqrt(2))^(n+1) / sqrt((1+sqrt(2))*Pi*n). - _Vaclav Kotesovec_, Feb 16 2015
%p a:= proc(n) option remember; `if`(n<2, 4*n+1, (12*(4*n-1)*(2*n-1)*(n-1)^2*
%p 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)))
%p end:
%p seq(a(n), n=0..40); # _Alois P. Heinz_, Jan 23 2023
%t 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 *)
%Y Cf. A000105, A126764.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 23 2007
|
