%I
%S 1,1,4,10,28,75,202,540,1440,3828,10153,26875,71021,187421,494013,
%T 1300844,3422509,8998118,23642479,62088032,162978242,427648023,
%U 1121766397,2941697012,7712415568,20215976824,52981414253,138831400836
%N Number of directed columnconvex polyominoes having at least one 1cell column.
%C a(n) = Fibonacci(2n1)  A121469(n,0) (obviously, since A121469(n,k) is the number of directed columnconvex polyominoes of area n having k 1cell columns). Column 1 of A121301.
%H E. Barcucci, R. Pinzani and R. Sprugnoli, <a href="http://dx.doi.org/10.1007/3540566104_71">Directed columnconvex polyominoes by recurrence relations</a>, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282298.
%F G.f.: z(1z)(13z+2z^2)/[(13z+z^2)(12zz^2+z^3)].
%e a(3)=4 because, with the exception of the 3cell column, all the other four directed columnconvex polyominoes of area 3 have a 1cell column.
%p G:=z*(1z)*(13*z+2*z^2)/(13*z+z^2)/(12*zz^2+z^3): Gser:=series(G,z=0,35): seq(coeff(Gser,z,n),n=1..32);
%o (PARI) Vec(z*(1z)*(13*z+2*z^2)/((13*z+z^2)*(12*zz^2+z^3)) + O(z^40)) \\ _Michel Marcus_, Feb 14 2016
%Y Cf. A121469, A121301.
%K nonn
%O 1,3
%A _Emeric Deutsch_, Aug 04 2006
