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A242544 Number of length n+3 0..3 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..3 introduced in 0..3 order.

%I A242544 #8 Jul 23 2025 11:17:13
%S A242544 13,42,150,554,2072,7808,29536,111878,423969,1607058,6092367,23097242,
%T A242544 87566957,331989206,1258663594,4771951574,18091832688,68591328768,
%U A242544 260049450816,985922294306,3737915147525,14171512153838,53728281674119
%N A242544 Number of length n+3 0..3 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..3 introduced in 0..3 order.
%C A242544 Column 3 of A242549
%H A242544 R. H. Hardin, <a href="/A242544/b242544.txt">Table of n, a(n) for n = 1..210</a>
%F A242544 Empirical: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -2*a(n-4) -12*a(n-5) -9*a(n-6) -18*a(n-7) -9*a(n-8).
%F A242544 Empirical: G.f.: -x*(-13+10*x-21*x^2+50*x^3+88*x^4+78*x^5+99*x^6+42*x^7) / ( (x^2+x-1)*(3*x^2+3*x-1)*(3*x^2+1)*(x^2+1) ). - _R. J. Mathar_, May 18 2014
%e A242544 Some solutions for n=4
%e A242544 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242544 ..1....1....0....1....1....0....1....1....1....1....1....1....1....1....1....1
%e A242544 ..2....2....1....1....1....1....1....1....1....0....1....2....2....2....2....2
%e A242544 ..1....1....2....0....2....0....2....2....2....0....2....3....1....0....1....3
%e A242544 ..2....1....3....2....0....2....0....3....3....2....1....0....2....0....0....1
%e A242544 ..2....1....0....0....1....3....0....3....3....1....3....2....0....3....1....0
%e A242544 ..1....2....3....0....2....1....3....0....3....2....3....2....3....1....1....0
%K A242544 nonn
%O A242544 1,1
%A A242544 _R. H. Hardin_, May 17 2014