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%I #10 Oct 16 2017 12:22:37
%S 42,343,1528,4917,12890,29325,60112,113745,201994,340659,550408,
%T 857701,1295802,1905881,2738208,3853441,5324010,7235599,9688728,
%U 12800437,16706074,21561189,27543536,34855185,43724746,54409707,67198888,82415013
%N Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors or less than both neighbors.
%C Row 5 of A200871.
%H R. H. Hardin, <a href="/A200875/b200875.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/2520)*n^7 + (17/180)*n^6 + (281/180)*n^5 + (64/9)*n^4 + (4927/360)*n^3 + (2303/180)*n^2 + (604/105)*n + 1.
%F Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F G.f.: x*(42 + 7*x - 40*x^2 - 55*x^3 + 70*x^4 - 29*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=3
%e ..2....0....1....2....0....3....2....3....2....2....1....0....3....2....0....3
%e ..0....3....1....2....3....3....2....0....3....1....1....0....0....1....0....2
%e ..0....3....3....0....3....2....0....0....3....1....0....0....0....1....1....2
%e ..1....1....3....0....2....2....0....0....3....3....0....2....0....2....1....1
%e ..2....1....3....3....0....1....2....1....0....3....1....2....0....3....0....1
%e ..2....1....3....3....0....1....2....1....0....3....1....2....3....3....0....1
%e ..1....3....1....0....1....1....3....1....0....3....3....3....3....3....0....2
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011