A006801 Number of 2-dimensional directed compact animals of size n.

1, 2, 5, 13, 34, 90, 239, 635, 1689, 4494, 11960, 31832, 84727, 225524, 600302, 1597904, 4253371, 11321838, 30137079, 80220557, 213535632, 568401380, 1513003529

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

Directed d- diagonally convex polyominoes. - David Bevan, Mar 15 2011

Examples

			a(3)=5: the six fixed trominoes excluding one orientation of the L tromino. - _David Bevan_, Mar 15 2011
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• V. K. Bhat et al., Enumeration of directed compact site animals in two dimensions, J. Phys. A 19 (1986), 3261-3265.

Crossrefs

Cf. A187276 (d- diagonally convex polyominoes).

Programs

Mathematica

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 *)

Extensions

Name and offset corrected, and more terms added by David Bevan, Mar 15 2011