%I #13 Sep 15 2019 19:58:34

%S 0,1,2,4,6,9,12,17,20

%N a(n) is the number of cells in the smallest polyomino that can contain all free n-ominoes.

%C a(n) <= n*(n - 1)/2 for n > 1, by using a right triangular polyomino with the topmost cell moved to the bottom row.

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%C Conjecture: a(9) = 26, a(10) = 31, a(11) = 37, and a(12) = 43.

%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/167484/53884">Smallest region of the plane that contains all free n-ominoes</a>

%e For n = 5 the smallest polyomino that contains all 5-ominos is a polyomino with a(5) = 9 cells. One such 9-omino that works is

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%e For example, the "L"-shaped, "+"-shaped, and "I"-shaped 5-ominoes fit in the following ways:

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%e All other 5-ominoes can fit into this 9-omino too.

%Y Cf. A000105.

%K nonn,more

%O 0,3

%A _Peter Kagey_, Sep 13 2019