%I
%S 10,22,43,82,157,304,586,1129,2176,4195,8086,15586,30043,57910,111625,
%T 215164,414742,799441,1540972,2970319,5725474,11036206,21272971,
%U 41004970,79039621,152353768,293671330,566069689,1091134408,2103229195,4054104622
%N Number of length n+3+1 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+2 elements, and new values 0..3 introduced in order.
%C Column 3 of A242239.
%H R. H. Hardin, <a href="/A242234/b242234.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n1) +a(n2) +a(n3) +a(n4).
%F Conjecture: a(n) = 9*A145112(n1) + A016777(n1).  _R. J. Mathar_, Aug 16 2017
%F Empirical g.f.: x*(10 + 12*x + 11*x^2 + 7*x^3) / (1  x  x^2  x^3  x^4).  _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....0....1....1....1....1....0....1....1....1....1....1
%e ..1....2....2....2....2....1....2....0....1....0....1....2....2....2....2....0
%e ..2....1....3....3....0....2....3....2....2....2....2....0....0....3....1....2
%e ..3....3....0....0....3....3....0....3....3....3....3....3....3....0....3....3
%e ..0....0....1....3....1....0....2....0....0....0....0....1....2....1....0....1
%e ..2....2....2....1....2....0....1....1....1....1....1....2....1....2....2....3
%e ..1....1....3....2....2....1....2....1....2....2....1....0....0....3....0....0
%e ..1....3....0....2....0....2....3....2....1....3....2....2....0....3....1....2
%Y Cf. A016777, A145112, A242239.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 08 2014
