|
|
A006801
|
|
Number of 2-dimensional directed compact animals of size n.
(Formerly M1440)
|
|
1
|
|
|
1, 2, 5, 13, 34, 90, 239, 635, 1689, 4494, 11960, 31832, 84727, 225524, 600302, 1597904, 4253371, 11321838, 30137079, 80220557, 213535632, 568401380, 1513003529
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Directed d- diagonally convex polyominoes. [David Bevan, Mar 15 2011]
|
|
REFERENCES
|
V. K. Bhat et al., Enumeration of directed compact site animals in two dimensions, J. Phys. A 19 (1986), 3261-3265.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
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).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Name and offset corrected, and more terms added by David Bevan, Mar 15 2011.
|
|
STATUS
|
approved
|
|
|
|