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A242317 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.

%I A242317 #9 Mar 19 2018 12:36:40
%S A242317 25,61,145,337,781,1829,4269,9957,23233,54225,126533,295265,689021,
%T A242317 1607877,3752057,8755625,20431737,47678569,111260509,259632437,
%U A242317 605866385,1413822053,3299230409,7698933081,17965877829,41924350093,97832744293
%N A242317 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 A242317 Column 2 of A242322.
%H A242317 R. H. Hardin, <a href="/A242317/b242317.txt">Table of n, a(n) for n = 1..210</a>
%F A242317 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 A242317 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 A242317 Some solutions for n=5:
%e A242317 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242317 ..1....1....1....1....1....1....1....1....1....0....1....0....0....1....1....1
%e A242317 ..0....2....1....2....1....0....2....1....0....1....0....1....1....0....1....2
%e A242317 ..1....2....2....0....2....1....2....2....0....2....2....1....0....2....0....0
%e A242317 ..2....0....0....1....0....2....2....2....2....2....2....2....2....1....2....1
%e A242317 ..1....2....2....0....2....0....0....0....1....0....1....2....2....2....1....2
%e A242317 ..1....1....1....2....2....1....1....1....0....1....2....0....2....0....2....1
%e A242317 ..0....1....2....2....1....1....1....0....0....2....0....1....1....2....0....2
%e A242317 ..0....0....2....0....2....0....2....0....1....2....2....0....0....0....2....0
%Y A242317 Cf. A242322.
%K A242317 nonn
%O A242317 1,1
%A A242317 _R. H. Hardin_, May 10 2014