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A365621
Minimum size of a set of polyominoes with n cells such that all other free polyominoes with n cells can be obtained by moving one cell of one of the polyominoes in the set.
1
1, 1, 1, 1, 2, 3, 7
OFFSET
1,5
COMMENTS
a(n) is the domination number of the n-omino graph defined in A098891.
The intermediate (the set of cells remaining when the cell to be moved is detached) does not have to be a connected (n-1)-omino.
a(8) <= 18, a(9) <= 53.
Apparently, a(n) is close to A367441(n-1) for 3 <= n <= 9. Is this just a coincidence?
EXAMPLE
For n <= 3, any one polyomino with n cells is enough to construct the others (if any) by moving one cell, so a(n) = 1.
For n = 4, either the L or the T tetromino suffices to construct the other four, so a(4) = 1.
Below are examples of sets of a(n) polyominoes that are sufficient to construct all other polyominoes with n cells, 5 <= n <= 7:
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CROSSREFS
KEYWORD
nonn,more
AUTHOR
STATUS
approved