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%I #8 Nov 10 2018 04:40:13
%S 20,125,440,1153,2524,4893,8688,14433,22756,34397,50216,71201,98476,
%T 133309,177120,231489,298164,379069,476312,592193,729212,890077,
%U 1077712,1295265,1546116,1833885,2162440,2535905,2958668,3435389,3971008,4570753
%N Number of length 3+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
%H R. H. Hardin, <a href="/A249709/b249709.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/15)*n^5 + 2*n^4 + 7*n^3 + 7*n^2 + (44/15)*n + 1.
%F Conjectures from _Colin Barker_, Nov 10 2018: (Start)
%F G.f.: x*(20 + 5*x - 10*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=6:
%e ..3....3....1....1....0....6....3....0....6....0....1....2....5....0....1....2
%e ..6....4....0....0....3....3....4....1....3....5....5....5....2....2....6....5
%e ..0....3....1....0....4....3....4....1....1....1....3....6....2....1....3....5
%e ..3....3....1....0....3....3....4....1....3....1....3....5....2....1....3....6
%e ..3....3....2....2....3....3....4....0....3....1....3....5....5....0....1....4
%e ..6....6....1....0....0....5....1....3....6....6....1....3....0....2....4....5
%Y Row 3 of A249707.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 04 2014