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 A367441 #17 Sep 18 2024 14:24:46 %S A367441 1,1,2,4,8,19 %N A367441 Minimum size of a set of polyominoes with n-1 cells such that all free polyominoes with n cells can be obtained by adding one cell to one of the polyominoes in the set. %C A367441 a(8) <= 54, a(9) <= 160. %C A367441 Apparently, a(n) is close to A365621(n+1) for n <= 8. Is this just a coincidence? %H A367441 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %e A367441 For n <= 4, all polyominoes with n-1 cells are needed to obtain all polyominoes with n cells by adding one cell, so a(n) = A000105(n-1). %e A367441 For n = 5, all but the square tetromino are needed to obtain all pentominoes, so a(5) = A000105(4)-1 = 4. %e A367441 For n = 6, there are 5 different sets of a(6) = 8 pentominoes that are sufficient to obtain all hexominoes. One of these sets consists of the I, L, N, P, U, V, W, and Y pentominoes. The X pentomino is the only pentomino that does not appear in any of these sets. The I, L, N, and W pentominoes are needed in all such sets. %e A367441 For n = 7, there are 8 different sets of a(7) = 19 hexominoes that are sufficient to obtain all heptominoes. 14 hexominoes appear in all these sets, 10 appear in none of them. %Y A367441 Cf. A000105, A365621, A367435, A367440, A367443. %K A367441 nonn,more %O A367441 2,3 %A A367441 _Pontus von Brömssen_, Nov 18 2023