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 A208638 #40 Sep 26 2021 14:10:47 %S A208638 4,13,32,71,150,309,628,1267,2546,5105,10224,20463,40942,81901,163820, %T A208638 327659,655338,1310697,2621416,5242855,10485734,20971493,41943012, %U A208638 83886051,167772130,335544289,671088608,1342177247,2684354526,5368709085 %N A208638 Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors. %C A208638 Row 3 of A208637. Possibly row 4 of the convolution array A213568. - _Clark Kimberling_, Jun 20 2012 %C A208638 From _Noah Carey_, Aug 31 2021: (Start) %C A208638 Conjecture: a(n) is equal to half the sum along the edges of (centered, height 2, width n, starting at line n+1) rectangles in Pascal's triangle, as shown here for n=3 (not including the terms inside the rectangles): %C A208638 1 %C A208638 1 1 %C A208638 1 2 1 a(3) = (4+6+4 + 15+20+15)/2 %C A208638 1 3 3 1 %C A208638 1 4---6---4 1 %C A208638 1 5 | | 5 1 %C A208638 1 6 15--20--15 6 1 %C A208638 1 7 21 35 35 20 7 1 (End) %H A208638 R. H. Hardin, <a href="/A208638/b208638.txt">Table of n, a(n) for n = 1..210</a> %F A208638 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). %F A208638 Conjectures from _Colin Barker_, Mar 07 2018: (Start) %F A208638 G.f.: x*(4 - 3*x) / ((1 - x)^2*(1 - 2*x)). %F A208638 a(n) = 5*2^n - n - 5. %F A208638 (End) %e A208638 Some solutions for n=4: %e A208638 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 %e A208638 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 %e A208638 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 %Y A208638 Cf. A208637. %K A208638 nonn %O A208638 1,1 %A A208638 _R. H. Hardin_, Feb 29 2012