Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Mar 19 2018 12:36:47
%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(n-1) +a(n-2) +a(n-3) +a(n-4).
%F Conjecture: a(n) = 9*A145112(n-1) + A016777(n-1). - _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