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A200867 Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

%I A200867 #16 Oct 16 2017 12:21:53
%S A200867 65,195,567,1673,4917,14455,42479,124851,366959,1078565,3170093,
%T A200867 9317449,27385589,80491001,236577045,695341043,2043728099,6006871845,
%U A200867 17655239697,51891816107,152519060911,448280011791,1317572818499,3872575368989
%N A200867 Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%C A200867 Column 4 of A200871.
%H A200867 R. H. Hardin, <a href="/A200867/b200867.txt">Table of n, a(n) for n = 1..210</a>
%F A200867 Empirical: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +4*a(n-4) +a(n-6) +a(n-7).
%F A200867 Empirical g.f.: x*(65 + 47*x^2 + 102*x^3 + 10*x^4 + 30*x^5 + 25*x^6) / (1 - 3*x + x^2 - x^3 - 4*x^4 - x^6 - x^7). - _Colin Barker_, Oct 16 2017
%e A200867 Some solutions for n=3
%e A200867 ..0....1....4....1....1....0....4....0....2....0....2....0....3....4....4....4
%e A200867 ..0....4....2....2....4....1....4....0....3....0....2....1....4....1....0....4
%e A200867 ..2....4....2....2....4....1....4....1....3....1....0....4....4....0....0....1
%e A200867 ..2....4....3....1....2....3....2....1....2....3....0....4....3....0....2....1
%e A200867 ..3....3....3....1....2....4....1....1....1....4....1....2....1....3....3....0
%t A200867 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, 5}]; a[n_] := Sum[a[n, x, y], {x, 5}, {y, 5}]; Array[a, 25] (* _Giovanni Resta_, Mar 05 2014 *)
%K A200867 nonn
%O A200867 1,1
%A A200867 _R. H. Hardin_, Nov 23 2011