

A006801


Number of 2dimensional 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
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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), 32613265.
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<1k<1k(k+1)/2>n; a[1, 1]=1; a[n_, k_]:=a[n, k]=Sum[(jk+2)a[nk, j], {j, k1, nk}]; 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



