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 A268768 #7 Jan 14 2019 09:04:39 %S A268768 3,12,32,100,248,620,1456,3380,7656,17148,37920,83140,180824,390796, %T A268768 839824,1796180,3825352,8116764,17165568,36195300,76118840,159694252, %U A268768 334301552,698429300,1456510888,3032326460,6303262176,13083742980 %N A268768 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once. %H A268768 R. H. Hardin, <a href="/A268768/b268768.txt">Table of n, a(n) for n = 1..210</a> %F A268768 Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>5. %F A268768 Conjectures from _Colin Barker_, Jan 14 2019: (Start) %F A268768 G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2). %F A268768 a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1. %F A268768 (End) %e A268768 Some solutions for n=4: %e A268768 ..1..2. .0..1. .2..1. .0..1. .1..0. .2..1. .0..1. .1..1. .0..0. .2..1 %e A268768 ..2..2. .0..0. .2..2. .1..0. .0..1. .2..2. .0..0. .2..2. .0..0. .1..2 %e A268768 ..1..1. .1..0. .2..1. .0..0. .0..0. .1..2. .0..0. .2..2. .0..1. .2..2 %e A268768 ..0..0. .0..1. .1..2. .1..0. .0..1. .1..2. .1..1. .1..2. .1..0. .2..1 %Y A268768 Column 2 of A268774. %K A268768 nonn %O A268768 1,1 %A A268768 _R. H. Hardin_, Feb 13 2016