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%I #10 Oct 16 2017 09:57:36
%S 12,51,144,325,636,1127,1856,2889,4300,6171,8592,11661,15484,20175,
%T 25856,32657,40716,50179,61200,73941,88572,105271,124224,145625,
%U 169676,196587,226576,259869,296700,337311,381952,430881,484364,542675,606096,674917
%N Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.
%C Row 2 of A200886.
%H R. H. Hardin, <a href="/A200887/b200887.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/3)*n^4 + (7/3)*n^3 + (14/3)*n^2 + (11/3)*n + 1.
%F Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F G.f.: x*(12 - 9*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%F a(n) = (1+n)^2 * (3+5*n+n^2) / 3.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=3
%e ..3....1....0....0....3....1....3....1....2....2....0....1....3....1....3....2
%e ..2....1....1....0....1....1....1....0....2....3....3....0....3....3....3....0
%e ..1....3....1....2....2....0....3....1....2....3....3....0....2....3....1....2
%e ..1....3....0....3....3....1....3....2....2....3....2....2....2....0....2....2
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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