A243027 - OEIS

%I #8 Nov 01 2018 11:39:16

%S 12,32,85,226,601,1598,4249,11298,30041,79878,212393,564746,1501641,

%T 3992814,10616761,28229618,75061625,199586390,530693641,1411096922,

%U 3752060265,9976604734,26527463577,70535652418,187551977881,498694535334

%N Number of length n+3 0..2 arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..2 introduced in 0..2 order.

%H R. H. Hardin, <a href="/A243027/b243027.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3).

%F Empirical g.f.: x*(12 + 8*x + 9*x^2) / (1 - 2*x - x^2 - 2*x^3). - _Colin Barker_, Nov 01 2018

%e Some solutions for n=3:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....1....1....1....0....1....1....1....1....0....1....1....0....1....1

%e ..1....0....0....0....2....1....2....1....0....2....1....0....1....1....2....0

%e ..2....1....1....1....0....0....2....2....0....1....2....2....1....2....0....1

%e ..1....1....2....1....0....2....2....0....2....1....2....2....2....1....2....2

%e ..0....1....0....1....0....0....0....0....1....1....2....2....2....1....0....1

%Y Column 2 of A243033.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 29 2014