%I
%S 252,7168,69984,396745,1616636,5272892,14647808,36038649,80620540,
%T 167049696,324977632,599664273,1057895164,1795425260,2946189056,
%U 4693534097,7283752188,11042199904,16392317280,23877870841,34188764412
%N Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some three terms equal to the minimum of the remaining four terms.
%H R. H. Hardin, <a href="/A250376/b250376.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (3/7)*n^8 + (57/7)*n^7 + (141/4)*n^6 + (202/3)*n^5 + (147/2)*n^4 + 44*n^3 + (443/28)*n^2 + (137/21)*n + 1.
%F Conjectures from _Colin Barker_, Nov 13 2018: (Start)
%F G.f.: x*(252 + 4900*x + 14544*x^2 + 3769*x^3  5005*x^4  1252*x^5 + 80*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....2....1....3....1....1....0....3....3....0....3....1....0....0....0....3
%e ..2....2....1....2....3....1....1....2....1....3....2....1....1....0....0....3
%e ..1....3....1....0....2....0....1....1....3....2....2....0....1....3....0....1
%e ..2....2....0....3....1....1....0....0....2....3....0....2....3....0....0....1
%e ..2....3....0....2....2....3....1....3....1....2....1....1....3....0....0....0
%e ..1....1....0....2....0....3....2....0....2....2....2....2....1....0....1....1
%e ..0....1....0....2....0....2....2....1....3....3....3....2....0....0....2....2
%e ..1....3....2....2....1....0....1....2....3....1....2....1....0....3....1....3
%e ..2....2....0....3....3....1....1....2....1....1....3....1....2....2....0....3
%Y Row 3 of A250373.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2014
