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 A365621 #21 Nov 19 2023 11:36:10 %S A365621 1,1,1,1,2,3,7 %N A365621 Minimum size of a set of polyominoes with n cells such that all other free polyominoes with n cells can be obtained by moving one cell of one of the polyominoes in the set. %C A365621 a(n) is the domination number of the n-omino graph defined in A098891. %C A365621 The intermediate (the set of cells remaining when the cell to be moved is detached) does not have to be a connected (n-1)-omino. %C A365621 a(8) <= 18, a(9) <= 53. %C A365621 Apparently, a(n) is close to A367441(n-1) for 3 <= n <= 9. Is this just a coincidence? %H A365621 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %e A365621 For n <= 3, any one polyomino with n cells is enough to construct the others (if any) by moving one cell, so a(n) = 1. %e A365621 For n = 4, either the L or the T tetromino suffices to construct the other four, so a(4) = 1. %e A365621 Below are examples of sets of a(n) polyominoes that are sufficient to construct all other polyominoes with n cells, 5 <= n <= 7: %e A365621 _ %e A365621 | | _ %e A365621 | |_ | |_ %e A365621 | _| | | %e A365621 |_| |_ _| %e A365621 _ %e A365621 | | _ %e A365621 | | | | _ _ %e A365621 | | | |_ _| _| %e A365621 | |_ | | | | %e A365621 |_ _| |_ _| |_ _| %e A365621 _ %e A365621 | | _ %e A365621 | | _ _ _ | | _ _ %e A365621 | | | |_ | |_ | | | |_ _ _| | | | %e A365621 | |_ | _| |_ | _| |_ _| _| _| _ _| _ _| |_ %e A365621 | _| | |_ _ _| |_ | _| | _| | _| | _ _ _| %e A365621 |_| |_ _ _| |_ _ _| |_ _| |_| |_| |_| %Y A365621 Cf. A098891, A367123, A367124, A367127, A367441. %K A365621 nonn,more %O A365621 1,5 %A A365621 _Pontus von Brömssen_, Nov 14 2023