A242317 - OEIS

%I #9 Mar 19 2018 12:36:40

%S 25,61,145,337,781,1829,4269,9957,23233,54225,126533,295265,689021,

%T 1607877,3752057,8755625,20431737,47678569,111260509,259632437,

%U 605866385,1413822053,3299230409,7698933081,17965877829,41924350093,97832744293

%N Number of length n+2+2 0..2 arrays with every value 0..2 appearing at least once in every consecutive 2+3 elements, and new values 0..2 introduced in order.

%C Column 2 of A242322.

%H R. H. Hardin, <a href="/A242317/b242317.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-5) - a(n-6).

%F Empirical g.f.: x*(25 + 36*x + 34*x^2 + 20*x^3 - 18*x^4 - 13*x^5) / ((1 + x)*(1 - 2*x - 2*x^3 + x^5)). - _Colin Barker_, Mar 19 2018

%e Some solutions for n=5:

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

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

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

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

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

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

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

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

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

%Y Cf. A242322.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 10 2014