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A200868 Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

%I A200868 #22 Oct 16 2017 12:22:01
%S A200868 106,356,1168,3886,12890,42744,141688,469726,1557320,5163158,17117854,
%T A200868 56752072,188154290,623802050,2068138180,6856654898,22732385492,
%U A200868 75366392740,249867889178,828405870894,2746476505360,9105600837300
%N A200868 Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%C A200868 Column 5 of A200871.
%H A200868 R. H. Hardin, <a href="/A200868/b200868.txt">Table of n, a(n) for n = 1..210</a>
%F A200868 Empirical: a(n) = 3*a(n-1) + a(n-3) + 7*a(n-4) + 3*a(n-5) + 2*a(n-6) + 3*a(n-7) + a(n-8).
%F A200868 Empirical g.f.: 2*x*(53 + 19*x + 50*x^2 + 138*x^3 + 67*x^4 + 48*x^5 + 57*x^6 + 18*x^7) / (1 - 3*x - x^3 - 7*x^4 - 3*x^5 - 2*x^6 - 3*x^7 - x^8). - _Colin Barker_, Oct 16 2017
%e A200868 Some solutions for n=3
%e A200868 ..0....3....5....1....1....4....0....5....1....3....5....3....5....2....0....3
%e A200868 ..1....0....5....1....0....0....2....3....1....5....0....0....2....0....0....5
%e A200868 ..4....0....5....1....0....0....5....2....3....5....0....0....1....0....2....5
%e A200868 ..4....1....5....0....0....2....5....2....3....2....3....2....1....5....3....4
%e A200868 ..4....1....4....0....2....5....5....5....4....2....4....5....3....5....4....0
%t A200868 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, 6}]; a[n_] := Sum[a[n, x, y], {x, 6}, {y, 6}]; Array[a, 25] (* _Giovanni Resta_, Mar 06 2014 *)
%K A200868 nonn
%O A200868 1,1
%A A200868 _R. H. Hardin_, Nov 23 2011