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A327094
a(n) is the number of cells in the smallest polyomino that can contain all free n-ominoes.
1
0, 1, 2, 4, 6, 9, 12, 17, 20
OFFSET
0,3
COMMENTS
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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Conjecture: a(9) = 26, a(10) = 31, a(11) = 37, and a(12) = 43.
EXAMPLE
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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#####.
#
For example, the "L"-shaped, "+"-shaped, and "I"-shaped 5-ominoes fit in the following ways:
+---+---+---+
| * * * |
+---+ +---+
| * |
+---+---+---+ +---+
| * |
+---+
.
+---+---+---+
| * |
+---+ +---+
| * * * |
+---+---+---+ +---+
| * |
+---+
.
+---+---+---+
| |
+---+ +---+
| * * * * * |
+---+---+---+ +---+
| |
+---+
All other 5-ominoes can fit into this 9-omino too.
CROSSREFS
Cf. A000105.
Sequence in context: A022778 A156022 A224809 * A048171 A090178 A080548
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Sep 13 2019
STATUS
approved