%I #14 Oct 16 2017 12:22:07
%S 161,595,2163,7973,29325,107777,395929,1454643,5344795,19638715,
%T 72159035,265134245,974183489,3579448271,13151993143,48324463973,
%U 177558916493,652405957937,2397139747601,8807827288183,32362661242755,118910351874471
%N Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%C Column 6 of A200871.
%H R. H. Hardin, <a href="/A200869/b200869.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) -3*a(n-2) +4*a(n-3) +9*a(n-4) +7*a(n-6) +6*a(n-7) +a(n-8) +2*a(n-9) +a(n-10).
%F Empirical g.f.: x*(161 - 49*x + 266*x^2 + 462*x^3 + 93*x^4 + 389*x^5 + 310*x^6 + 70*x^7 + 105*x^8 + 49*x^9) / (1 - 4*x + 3*x^2 - 4*x^3 - 9*x^4 - 7*x^6 - 6*x^7 - x^8 - 2*x^9 - x^10). - _Colin Barker_, Oct 16 2017
%e Some solutions for n=3
%e ..6....3....0....5....3....0....6....6....2....5....5....2....6....0....5....5
%e ..6....2....4....1....3....0....6....2....3....2....3....0....4....1....0....2
%e ..5....2....4....0....2....6....6....2....5....2....1....0....0....1....0....2
%e ..3....3....4....0....2....6....1....3....5....1....1....3....0....2....2....6
%e ..2....4....4....5....5....3....0....6....4....0....3....3....0....5....3....6
%t a[0,x_,y_] := 1; a[n_,x_,y_] := a[n,x,y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 7}]; a[n_] := Sum[a[n, x, y], {x, 7}, {y, 7}]; Array[a, 25] (* _Giovanni Resta_, Mar 05 2014 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011