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 A281200 #12 Jul 06 2024 10:24:56 %S A281200 1,14,56,168,448,1120,2688,6272,14336,32256,71680,157696,344064, %T A281200 745472,1605632,3440640,7340032,15597568,33030144,69730304,146800640, %U A281200 308281344,645922816,1350565888,2818572288,5872025600,12213813248,25367150592 %N A281200 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. %H A281200 R. H. Hardin, <a href="/A281200/b281200.txt">Table of n, a(n) for n = 1..210</a> %H A281200 Sela Fried, <a href="https://arxiv.org/abs/2406.18923">Counting r X s rectangles in nondecreasing and Smirnov words</a>, arXiv:2406.18923 [math.CO], 2024. See p. 12. %F A281200 Empirical: a(n) = 4*a(n-1) - 4*a(n-2) for n>3. %F A281200 Conjectures from _Colin Barker_, Feb 16 2019: (Start) %F A281200 G.f.: x*(1 + 10*x + 4*x^2) / (1 - 2*x)^2. %F A281200 a(n) = 7*2^(n-1) * (n-1) for n>1. %F A281200 (End) %e A281200 Some solutions for n=4: %e A281200 ..0..1..0. .0..1..1. .0..0..1. .0..1..0. .0..0..1. .0..0..0. .0..1..1 %e A281200 ..1..1..0. .0..1..0. .1..0..1. .0..1..1. .1..1..0. .1..1..0. .1..0..1 %e A281200 ..0..1..0. .0..1..0. .1..0..1. .1..0..1. .0..1..0. .0..1..0. .1..0..1 %e A281200 ..0..1..0. .0..1..0. .1..1..0. .1..0..0. .0..1..0. .0..1..1. .0..1..0 %Y A281200 Column 3 of A281205. %K A281200 nonn %O A281200 1,2 %A A281200 _R. H. Hardin_, Jan 17 2017