This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A283056 #11 Feb 27 2017 21:38:10 %S A283056 0,7,9,11,11,13,13 %N A283056 Size of the smallest polyomino that admits a hole of size n. %C A283056 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. %C A283056 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. %C A283056 Perhaps a(n) is actually equal to A027709(n)+3? %e A283056 For n=1, we have a single square hole, so a(1)=7. %e A283056 For n=2, we have a domino hole, so a(2)=9. %e A283056 For n=3, we can use either an L or V tromino hole, so a(3)=11. %e A283056 For n=4, we use the square tetromino hole, so a(4)=11. %e A283056 For n=5, we use the P pentomino hole, so a(5)=13. %e A283056 For n=6, we use the 2 X 3 rectangle hole, so a(6)=13. %Y A283056 Cf. A027709. %K A283056 nonn,more %O A283056 0,2 %A A283056 _Dmitry Kamenetsky_, Feb 27 2017