# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a243515 Showing 1-1 of 1 %I A243515 #8 Nov 02 2018 12:26:53 %S A243515 3,5,10,25,77,279,1134,4979,22981,109453,531458,2610933,12917685, %T A243515 64181627,319695982,1594859887,7963472189,39784944801,198827606706, %U A243515 993846943841,4968361974493,24839192686975,124188113975630 %N A243515 Number of length n+2 0..6 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..6 introduced in 0..6 order. %H A243515 R. H. Hardin, Table of n, a(n) for n = 1..210 %F A243515 Empirical: a(n) = 12*a(n-1) - 52*a(n-2) + 102*a(n-3) - 91*a(n-4) + 30*a(n-5). %F A243515 Conjectures from _Colin Barker_, Nov 02 2018: (Start) %F A243515 G.f.: x*(3 - 31*x + 106*x^2 - 141*x^3 + 60*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)). %F A243515 a(n) = (147 + 2^(5+n) + 4*3^(1+n) + 5^n + 36*n) / 96. %F A243515 (End) %e A243515 All solutions for n=3: %e A243515 ..0....0....0....0....0....0....0....0....0....0 %e A243515 ..1....0....1....0....1....1....0....1....0....0 %e A243515 ..2....1....2....0....2....2....0....2....1....0 %e A243515 ..3....2....3....1....0....3....0....0....2....0 %e A243515 ..1....0....0....2....3....4....1....1....3....0 %Y A243515 Column 6 of A243519. %K A243515 nonn %O A243515 1,1 %A A243515 _R. H. Hardin_, Jun 05 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE