%I M1440 #17 Jan 08 2018 01:58:27
%S 1,2,5,13,34,90,239,635,1689,4494,11960,31832,84727,225524,600302,
%T 1597904,4253371,11321838,30137079,80220557,213535632,568401380,
%U 1513003529
%N Number of 2-dimensional directed compact animals of size n.
%C Directed d- diagonally convex polyominoes. [David Bevan, Mar 15 2011]
%D V. K. Bhat et al., Enumeration of directed compact site animals in two dimensions, J. Phys. A 19 (1986), 3261-3265.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%e a(3)=5: the six fixed trominoes excluding one orientation of the L tromino. [David Bevan, Mar 15 2011]
%t a[n_,k_]:=0/;n<1||k<1||k(k+1)/2>n; a[1,1]=1; a[n_,k_]:=a[n,k]=Sum[(j-k+2)a[n-k,j],{j,k-1,n-k}]; a[n_]:=Sum[a[n,k],{k,n}]; Array[a,30] (* David Bevan, Mar 15 2011 *)
%Y Cf. A187276 (d- diagonally convex polyominoes).
%K nonn
%O 1,2
%A _N. J. A. Sloane_.
%E Name and offset corrected, and more terms added by _David Bevan_, Mar 15 2011.