%I #8 Nov 11 2018 09:55:50
%S 144,2228,15472,68863,232096,647122,1572320,3441309,6938416,13092816,
%T 23393360,39926107,65536576,104018734,160332736,240853433,353651664,
%U 508810348,718777392,998757431,1367144416,1845997066,2461559200
%N Number of length 3+5 0..n arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms.
%H R. H. Hardin, <a href="/A250084/b250084.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/5)*n^7 + (19/3)*n^6 + (47/2)*n^5 + 37*n^4 + (183/5)*n^3 + (83/3)*n^2 + (23/2)*n + 1.
%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)
%F G.f.: x*(144 + 1076*x + 1680*x^2 - 593*x^3 - 280*x^4 - 18*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=4:
%e ..0....2....4....2....2....2....3....3....4....3....2....4....3....1....3....0
%e ..2....4....2....4....0....3....2....2....0....3....3....1....1....1....1....1
%e ..0....4....1....0....0....0....4....0....0....3....2....4....1....1....1....0
%e ..3....0....4....0....1....1....4....2....1....0....2....2....2....1....4....1
%e ..0....0....1....0....0....1....0....4....0....4....1....2....3....1....4....0
%e ..0....0....1....3....4....2....2....2....4....3....4....2....0....3....0....4
%e ..0....0....3....0....1....2....3....4....3....3....3....2....1....3....1....0
%e ..3....4....1....2....0....2....2....2....0....4....4....2....4....0....2....0
%Y Row 3 of A250081.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 11 2014