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A242234 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. 2

%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(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

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Last modified June 13 05:11 EDT 2021. Contains 344981 sequences. (Running on oeis4.)