A006801 Number of 2-dimensional directed compact animals of size n. (Formerly M1440)

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

Offset

1,2

Comments

Directed d- diagonally convex polyominoes. - 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

Table of n, a(n) for n=1..23.

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

Example

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

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 *)

Crossrefs

Cf. A187276 (d- diagonally convex polyominoes).

Sequence in context: A112842 A097417 A367657 * A329674 A114173 A238435

Adjacent sequences: A006798 A006799 A006800 * A006802 A006803 A006804

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved