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 A322150 #6 Nov 28 2018 22:36:13 %S A322150 1,4,6,74,6,900,3230 %N A322150 Number of minimum shadings of an n X n Hitori solution grid as defined in A322125. %C A322150 Equivalently, the number of n X n binary matrices with the least possible number of 1's such that all 0's are connected and no 1 is adjacent to another and that it is not possible to set another 1 without either placing it adjacent to another 1 or disconnecting the 0's. The least possible number of 1's is given by A322125(n). %e A322150 Case n=3: a(3) = 6: up to rotation and reflection there are 2 solutions: %e A322150 X . . : . X . %e A322150 . X . : . . . %e A322150 . . . : . X . %e A322150 . %e A322150 Case n=5: a(5) = 6: up to rotation and reflection there are 2 solutions: %e A322150 . . X . . : . . . X . %e A322150 . X . X . : X . . . . %e A322150 . . . . . : . . X . . %e A322150 . . . . . : . . . . X %e A322150 . X . X . : . X . . . %e A322150 . %e A322150 For an n X m grid the number of minimum shadings are as follows: %e A322150 ====================================================== %e A322150 n\m| 1 2 3 4 5 6 7 8 9 10 11 12 %e A322150 ---+-------------------------------------------------- %e A322150 1 | 1 2 1 1 1 1 1 1 1 1 1 1 ... %e A322150 2 | 2 4 2 12 12 4 48 32 8 160 80 16 ... %e A322150 3 | 1 2 6 1 13 53 11 100 6 113 2 88 ... %e A322150 4 | 1 12 1 74 11 44 139 512 1745 5764 19209 96 ... %e A322150 5 | 1 12 13 11 6 3 2035 ... %e A322150 6 | 1 4 53 44 3 900 90 ... %e A322150 ... %e A322150 An interesting tight solution set occurs with the 5 X 6 grid. The 3 solutions are: %e A322150 . X . . . : . . X . . : . . . X . %e A322150 . . . . X : . X . X . : X . . . . %e A322150 . . . X . : . . . . . : . X . . . %e A322150 . X . . . : . . . . . : . . . X . %e A322150 X . . . . : . X . X . : . . . . X %e A322150 . . . X . : . . X . . : . X . . . %Y A322150 Cf. A322125. %K A322150 nonn,hard,more %O A322150 1,2 %A A322150 _Andrew Howroyd_, Nov 28 2018