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%I #8 Nov 12 2018 14:35:26
%S 193,3450,26710,129595,468231,1382188,3522460,8028405,16761565,
%T 32604286,59831058,104560495,175295875,283562160,444647416,678456553,
%U 1010485305,1472922370,2105887630,2958814371,4091983423,5578217140,7504741140
%N Number of length 2+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="/A250156/b250156.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (11/7)*n^7 + 13*n^6 + (67/2)*n^5 + (97/2)*n^4 + (103/2)*n^3 + 34*n^2 + (139/14)*n + 1.
%F Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F G.f.: x*(193 + 1906*x + 4514*x^2 + 1707*x^3 - 339*x^4 - 68*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....3....3....2....3....2....1....1....3....2....0....2....2....3....3....0
%e ..1....1....2....4....3....0....2....3....3....1....2....2....1....2....0....3
%e ..1....0....2....2....2....0....0....0....4....2....0....2....2....0....4....0
%e ..1....2....2....3....2....4....3....3....1....1....1....2....3....2....4....2
%e ..4....1....2....1....3....0....3....1....1....4....0....3....1....0....1....3
%e ..3....2....4....2....0....0....0....0....1....1....4....2....0....0....1....0
%e ..4....3....0....2....3....4....0....0....3....1....0....1....1....2....1....0
%e ..0....3....4....3....4....2....4....4....2....0....0....2....1....3....3....0
%Y Row 2 of A250154.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2014
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