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 A381553 #10 Feb 28 2025 08:04:39 %S A381553 1,8,64,368,2776,25880,251704,2629080,28964248,331032312,3907675376, %T A381553 47392320240,587548108400,7421689479608,95248568409312, %U A381553 1239031994818680,16306127772957216,216760982171930144,2906731043068293952,39278080769921432856,534346120254755625336 %N A381553 Number of 2*n X 6 binary arrays with row sums 3 and column sums n, avoiding the patterns 010 and 101 in any row and column. %H A381553 Christoph Koutschan, <a href="/A381553/b381553.txt">Table of n, a(n) for n = 0..70</a> %H A381553 Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, <a href="https://ecajournal.haifa.ac.il/Volume2025/ECA2025_S2A14.pdf">The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices</a>, Enumerative Combinatorics and Applications 5:2, Article #S2R14, 2025. %e A381553 A few solutions for n = 3 are: %e A381553 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 %e A381553 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 %e A381553 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 %e A381553 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 %e A381553 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 %e A381553 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 %Y A381553 Cf. A381551, A381554. %K A381553 nonn %O A381553 0,2 %A A381553 _Christoph Koutschan_, Feb 27 2025