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%I #18 Oct 09 2023 15:26:45
%S 36,94,236,602,1528,3882,9858,25038,63592,161514,410218,1041884,
%T 2646208,6720920,17069998,43354902,110114102,279671154,710317326,
%U 1804085608,4582071648,11637685314,29557748082,75071670020,190669317026,484267746348,1229957991200,3123884816870
%N Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
%H R. H. Hardin, <a href="/A200866/b200866.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-4) +a(n-5).
%F Empirical g.f.: 2*x*(18 + 11*x + 6*x^2 + 18*x^3 + 8*x^4) / (1 - 2*x - x^2 - 2*x^4 - x^5). - _Colin Barker_, Oct 15 2017
%e Some solutions for n=3:
%e ..1....0....1....3....0....1....1....2....0....0....3....0....0....0....0....3
%e ..2....1....3....1....2....0....1....2....3....1....2....2....0....0....0....2
%e ..2....2....3....1....3....0....0....2....3....3....2....3....0....2....2....0
%e ..1....2....3....2....3....2....0....2....3....3....1....3....1....2....3....0
%e ..0....3....0....3....3....2....3....1....2....1....1....2....2....0....3....3
%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, 4}]; a[n_] := Sum[a[n, x, y], {x, 4}, {y, 4}]; Array[a, 25] (* _Giovanni Resta_, Mar 05 2014 *)
%Y Column 3 of A200871.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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