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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).
5

%I #4 Aug 13 2020 14:01:06

%S 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,

%T 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,

%U 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

%N 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).

%D 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.

%H E. J. Friedman, <a href="https://erich-friedman.github.io/mathmagic/0599.html">Math. Magic</a>

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

%e ..X..

%e .XXX.

%e ..X..

%Y Cf. A000105.

%K nonn

%O 0,1

%A Brendan Owen (bdowen(AT)ee.mu.oz.au)