A327094 a(n) is the number of cells in the smallest polyomino that can contain all free n-ominoes.

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.

Links

Table of n, a(n) for n=0..8.

Code Golf Stack Exchange, Smallest region of the plane that contains all free n-ominoes

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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  #####.
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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

Adjacent sequences: A327091 A327092 A327093 * A327095 A327096 A327097

Keyword

nonn,more

Author

Peter Kagey, Sep 13 2019

Status

approved