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%I #7 Nov 12 2018 15:39:53
%S 172,4409,37824,193437,725596,2210213,5794496,13561449,29037004,
%T 57870241,108719744,194381733,333198204,550785901,882129536,
%U 1374085265,2088343020,3104898889,4526091328,6481257581,9132069276,12678608757,17366250304
%N Number of length 4+5 0..n arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms.
%H R. H. Hardin, <a href="/A250340/b250340.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (9/140)*n^8 + (27/10)*n^7 + 19*n^6 + 48*n^5 + (1203/20)*n^4 + (1189/30)*n^3 + (81/14)*n^2 - (13/3)*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(172 + 2861*x + 4335*x^2 - 2703*x^3 - 2357*x^4 + 227*x^5 + 65*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=4:
%e ..1....1....0....2....2....1....0....1....1....1....1....1....0....0....1....0
%e ..4....1....0....2....1....4....2....2....2....2....0....2....2....1....3....4
%e ..2....0....2....0....1....0....2....1....1....3....2....2....4....2....1....4
%e ..3....1....4....4....3....4....2....2....0....3....4....2....2....2....2....4
%e ..2....1....3....3....2....2....4....2....1....3....3....0....0....2....1....4
%e ..0....2....2....0....2....2....3....3....4....4....2....4....4....3....1....4
%e ..2....2....2....2....4....2....1....4....1....1....2....2....2....2....1....2
%e ..4....0....1....2....0....4....1....0....3....0....1....2....2....4....1....4
%e ..0....1....1....1....0....0....2....2....0....3....1....3....3....1....0....4
%Y Row 4 of A250336.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2014
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