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 A381857 #17 Mar 15 2025 23:29:40 %S A381857 0,0,9,449,64302,33498985,68713877875,562948673292362, %T A381857 18446743413061588661,2417851638458709952150645, %U A381857 1267650600226199352445557225326,2658455991569819662405962686908743173,22300745198530622979053904922855772969397419 %N A381857 Number of n X n binary matrices with at least 2 adjacent 1's. %C A381857 Use black and white square tiles to fill an n X n grid. In some combinations, a black tile will share a side with another black tile. This sequence counts the number of arrangements containing at least one black tile sharing a side with another black tile. %F A381857 a(n) = 2^(n^2) - A006506(n). %e A381857 For n=1, there are no arrangements with two black tiles touching as there is only space for one tile. %e A381857 n=2 is a 2 X 2 grid, and there are 9 possible arrangements where at least two black tiles touch on an edge: %e A381857 00 01 10 11 01 10 11 11 11 %e A381857 11, 01, 10, 00, 11, 11, 01, 10, 11. %e A381857 n=3 is a 3 X 3 grid, and with 2^9=512 possible combinations of black and white tiles, 449 of them have at least two black tiles touching. %Y A381857 Cf. A002416, A006506. %K A381857 nonn %O A381857 0,3 %A A381857 _Benjamin Ghitterman_, Mar 08 2025