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 A269613 #7 Mar 21 2018 17:19:50 %S A269613 3,9,27,78,222,624,1740,4824,13320,36672,100752,276384,757344,2073600, %T A269613 5674176,15520128,42437760,116014080,317100288,866621952,2368230912, %U A269613 6471278592,17682164736,48313178112,132003268608,360658059264 %N A269613 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1. %C A269613 Column 2 of A269619. %H A269613 R. H. Hardin, <a href="/A269613/b269613.txt">Table of n, a(n) for n = 1..210</a> %F A269613 Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 4*a(n-3). %F A269613 Conjectures from _Colin Barker_, Mar 21 2018: (Start) %F A269613 G.f.: 3*x*(1 - x - x^2) / ((1 - 2*x)*(1 - 2*x - 2*x^2)). %F A269613 a(n) = (-3*2^n + (3-2*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(3+2*sqrt(3))) / 4. %F A269613 (End) %e A269613 Some solutions for n=8: %e A269613 ..1. .1. .0. .0. .0. .1. .1. .1. .2. .2. .2. .1. .1. .1. .0. .1 %e A269613 ..2. .1. .0. .0. .2. .2. .1. .2. .1. .0. .0. .0. .1. .2. .2. .0 %e A269613 ..2. .0. .0. .1. .2. .1. .0. .1. .2. .0. .2. .2. .2. .1. .0. .1 %e A269613 ..2. .1. .1. .2. .2. .1. .1. .1. .0. .2. .1. .1. .1. .2. .0. .0 %e A269613 ..2. .2. .2. .0. .1. .0. .1. .0. .1. .0. .1. .1. .0. .0. .1. .0 %e A269613 ..2. .0. .2. .2. .2. .0. .1. .1. .1. .0. .2. .2. .1. .2. .2. .1 %e A269613 ..1. .0. .1. .0. .1. .2. .0. .1. .1. .1. .0. .0. .1. .1. .2. .2 %e A269613 ..1. .0. .1. .2. .0. .1. .0. .1. .1. .2. .2. .1. .0. .2. .1. .1 %Y A269613 Cf. A269619. %K A269613 nonn %O A269613 1,1 %A A269613 _R. H. Hardin_, Mar 01 2016