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A283056 Size of the smallest polyomino that admits a hole of size n. 0
0, 7, 9, 11, 11, 13, 13 (list; graph; refs; listen; history; text; internal format)



The task here is to surround a hole of size n with the least number of squares. The hole is another polyomino, so we can obtain a lower bound using A027709: minimal perimeter of polyomino with n square cells. We need an extra 3 (or more) diagonal cells to surround any hole. Hence a(n) >= A027709(n) + 3 = 2*ceiling(2*sqrt(n)) + 3.

For rectangular holes we can obtain an upper bound using A262767: minimum perimeter of a rectangle with area n and integer sides. Hence a(n) <= A262767(n) + 3.

Perhaps a(n) is actually equal to A027709(n)+3?


Table of n, a(n) for n=0..6.


For n=1, we have a single square hole, so a(1)=7.

For n=2, we have a domino hole, so a(2)=9.

For n=3, we can use either an L or V tromino hole, so a(3)=11.

For n=4, we use the square tetromino hole, so a(4)=11.

For n=5, we use the P pentomino hole, so a(5)=13.

For n=6, we use the 2 X 3 rectangle hole, so a(6)=13.


Cf. A027709.

Sequence in context: A112162 A058483 A176326 * A162308 A191883 A108815

Adjacent sequences:  A283053 A283054 A283055 * A283057 A283058 A283059




Dmitry Kamenetsky, Feb 27 2017



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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)