%I #10 Oct 16 2017 12:22:46
%S 50,144,422,1268,3823,11472,34350,102896,308419,924532,2771101,
%T 8305373,24892609,74608516,223618304,670231838,2008825312,6020872062,
%U 18045827096,54087163859,162110668160,485879938474,1456284886944,4364793695063
%N Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.
%C Column 3 of A200886.
%H R. H. Hardin, <a href="/A200881/b200881.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7).
%F Empirical g.f.: x*(50 - 56*x + 146*x^2 - 56*x^3 + 93*x^4 - 12*x^5 + 16*x^6) / (1 - 4*x + 6*x^2 - 10*x^3 + 5*x^4 - 6*x^5 + x^6 - x^7). - _Colin Barker_, Oct 16 2017
%e Some solutions for n=3
%e ..2....2....2....3....0....3....1....1....3....3....1....3....0....1....3....1
%e ..0....2....1....2....0....3....1....2....2....3....0....3....1....1....1....2
%e ..2....1....0....0....2....3....0....2....1....1....1....1....3....0....3....3
%e ..2....2....0....1....3....3....2....0....2....1....2....0....3....0....3....3
%e ..0....2....2....2....3....2....3....3....3....2....3....3....1....3....3....3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011