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%I #8 Nov 09 2018 14:20:29
%S 14,69,208,485,966,1729,2864,4473,6670,9581,13344,18109,24038,31305,
%T 40096,50609,63054,77653,94640,114261,136774,162449,191568,224425,
%U 261326,302589,348544,399533,455910,518041,586304,661089,742798,831845,928656
%N Number of length 2+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="/A249708/b249708.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/2)*n^4 + 4*n^3 + (11/2)*n^2 + 3*n + 1.
%F Conjectures from _Colin Barker_, Nov 09 2018: (Start)
%F G.f.: x*(2 - x)*(7 + 3*x + 3*x^2 - x^3) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=6:
%e ..3....6....0....3....0....0....2....3....3....5....5....3....4....4....0....2
%e ..2....2....2....4....4....4....1....2....1....6....3....5....1....0....4....2
%e ..0....2....3....4....4....5....0....2....5....5....4....6....2....4....1....2
%e ..2....0....2....6....5....4....1....2....3....5....4....5....2....4....1....2
%e ..4....6....0....3....1....2....2....5....3....4....5....5....2....6....0....1
%Y Row 2 of A249707.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 04 2014
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