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 A381551 #18 Feb 28 2025 08:05:10 %S A381551 1,4,16,64,324,1764,10000,58564,350464,2131600,13133376,81757764, %T A381551 513294336,3245580900,20646241344,132021769104,848031024996, %U A381551 5468890936356,35392361925904,229761144199876,1495753923300484,9762043084514704,63858040015802256 %N A381551 Number of 2*n X 4 binary arrays with row sums 2 and column sums n, avoiding the patterns 010 and 101 in any row and column. %H A381551 Christoph Koutschan, <a href="/A381551/b381551.txt">Table of n, a(n) for n = 0..1000</a> %H A381551 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. %H A381551 Christoph Koutschan, <a href="/A381551/a381551.txt">Recurrence of order 10 with polynomial coefficients of degree 21</a>. %F A381551 a(n) ~ 4*phi^(4*n)/(Pi*sqrt(5)*n), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Feb 27 2025 %e A381551 Here are 5 out of 16 solutions for n = 2: %e A381551 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 %e A381551 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 %e A381551 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 %e A381551 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 %e A381551 the remaining ones are obtained from these by reflecting, rotating, or exchanging 0 and 1. %Y A381551 Cf. A381553, A381554. %K A381551 nonn %O A381551 0,2 %A A381551 _Christoph Koutschan_, Feb 27 2025