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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 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.)