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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).
Sequence in context: A112842 A097417 A367657 * A329674 A114173 A238435
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name and offset corrected, and more terms added by David Bevan, Mar 15 2011.
STATUS
approved

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Last modified May 28 12:54 EDT 2024. Contains 372913 sequences. (Running on oeis4.)