

A327094


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


0




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 nominoes


EXAMPLE

For n = 5 the smallest polyomino that contains all 5ominos is a polyomino with a(5) = 9 cells. One such 9omino that works is
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#####.
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For example, the "L"shaped, "+"shaped, and "I"shaped 5ominoes fit in the following ways:
++++
 * * * 
++ ++
 * 
++++ ++
 * 
++
.
++++
 * 
++ ++
 * * * 
++++ ++
 * 
++
.
++++
 
++ ++
 * * * * * 
++++ ++
 
++
All other 5ominoes can fit into this 9omino 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



