%I #8 Nov 12 2018 14:36:13
%S 354,8377,79740,455055,1879526,6219899,17519352,43657365,98808010,
%T 206916501,406440244,756627027,1345629390,2300780615,3801384176,
%U 6094394889,9513396402,14501306065,21637264620,31668194551,45545537334
%N Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some two terms equal to the minimum of the remaining five terms.
%H R. H. Hardin, <a href="/A250157/b250157.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (55/84)*n^8 + (67/7)*n^7 + (151/4)*n^6 + 70*n^5 + (1061/12)*n^4 + (521/6)*n^3 + (1377/28)*n^2 + (445/42)*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(354 + 5191*x + 17091*x^2 + 9231*x^3  4393*x^4  1117*x^5 + 51*x^6  9*x^7 + x^8) / (1  x)^9.
%F a(n) = 9*a(n1)  36*a(n2) + 84*a(n3)  126*a(n4) + 126*a(n5)  84*a(n6) + 36*a(n7)  9*a(n8) + a(n9) for n>9.
%F (End)
%e Some solutions for n=3:
%e ..0....3....0....1....2....1....1....3....2....0....1....0....2....3....1....3
%e ..1....0....3....3....1....0....1....1....0....3....2....2....2....1....1....3
%e ..0....1....3....0....0....3....1....0....3....3....1....0....0....3....1....1
%e ..2....3....2....3....0....1....3....1....1....3....3....0....0....3....0....1
%e ..0....3....2....1....0....0....2....1....1....0....0....3....2....0....2....1
%e ..0....1....2....0....1....2....2....3....2....1....3....3....0....0....3....3
%e ..3....1....3....0....0....0....1....3....1....0....1....0....1....0....2....3
%e ..0....3....3....0....1....0....1....1....2....0....2....2....1....2....1....1
%e ..2....1....0....0....0....1....2....2....1....1....1....2....2....1....3....3
%Y Row 3 of A250154.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2014
