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A327094 a(n) is the number of cells in the smallest polyomino that can contain all free n-ominoes. 0
0, 1, 2, 4, 6, 9, 12, 17, 20 (list; graph; refs; listen; history; text; internal format)
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.

   ##

   ###

   ####

  ######

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

   ###

  #####.

     #

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

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Last modified February 18 15:04 EST 2020. Contains 332019 sequences. (Running on oeis4.)