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A006801 Number of 2-dimensional directed compact animals of size n.
(Formerly M1440)
0
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

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

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: A114299 A112842 A097417 * A114173 A238435 A023425

Adjacent sequences:  A006798 A006799 A006800 * A006802 A006803 A006804

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified January 17 10:08 EST 2019. Contains 319218 sequences. (Running on oeis4.)