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%I #10 Oct 16 2017 12:22:22
%S 10,37,94,195,356,595,932,1389,1990,2761,3730,4927,6384,8135,10216,
%T 12665,15522,18829,22630,26971,31900,37467,43724,50725,58526,67185,
%U 76762,87319,98920,111631,125520,140657,157114,174965,194286,215155,237652,261859
%N Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.
%C Row 2 of A200871.
%H R. H. Hardin, <a href="/A200872/b200872.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/12)*n^4 + (3/2)*n^3 + (47/12)*n^2 + (7/2)*n + 1.
%F Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F G.f.: x*(10 - 13*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%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 ..1....0....2....0....3....0....2....2....1....0....0....0....3....0....3....0
%e ..2....2....3....1....3....0....2....2....3....2....0....0....2....2....1....1
%e ..2....3....3....1....2....1....1....2....3....2....0....1....2....2....1....3
%e ..1....3....0....0....1....1....0....2....1....1....0....2....2....0....1....3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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