E. J. Friedman, <a href="httphttps://wwwerich-friedman.stetsongithub.edu/~efriedmaio/mathmagic/0599.html">Math. Magic</a>

E. J. Friedman, <a href="http://www.stetson.edu/~efriedma/mathmagic/0599.html">Math. Magic</a>

nonn,new

nonn

Brendan Owen (bdowen@(AT)ee.mu.oz.au)

<a href="http://www.stetson.edu/~efriedma/mathmagic/0599.html">Math . Magic</a>

nonn,new

nonn

Size of smallest polyomino with surround number n (the surround number of a polyomino is the number of different ways that it can be surrounded by non-overlapping copies of the same polyomino).

7, 1, 5, 9, 8, 9, 9, 4, 8, 7, 9, 9, 9, 9, 8, 9, 6, 9, 8, 8, 9, 8, 8, 7, 9, 8, 7, 8, 8, 9, 8, 8, 9, 9, 8, 9, 9, 9, 9, 8, 9, 6, 8, 9, 10, 9, 9, 8, 6, 7, 8, 8, 8, 9, 8, 9, 9, 9, 10, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 7, 8, 8, 9, 9, 7, 8, 7, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 8, 9, 9, 9

0,1

W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

<a href="http://www.stetson.edu/~efriedma/mathmagic/0599.html">Math Magic</a>

a(2) = 5 because the smallest polyomino which has a surround number 2 is

..X..

.XXX.

..X..

Cf. A000105.

nonn

Brendan Owen (bdowen@ee.mu.oz.au)

approved