|
|
A327094
|
|
a(n) is the number of cells in the smallest polyomino that can contain all free n-ominoes.
|
|
1
|
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|