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%I #9 Oct 15 2017 01:11:41
%S 32,191,676,1817,4108,8239,15128,25953,42184,65615,98396,143065,
%T 202580,280351,380272,506753,664752,859807,1098068,1386329,1732060,
%U 2143439,2629384,3199585,3864536,4635567,5524876,6545561,7711652,9038143
%N Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases.
%C Row 3 of A200838.
%H R. H. Hardin, <a href="/A200840/b200840.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (4/15)*n^5 + (17/6)*n^4 + (28/3)*n^3 + (73/6)*n^2 + (32/5)*n + 1.
%F Conjectures from _Colin Barker_, Oct 14 2017: (Start)
%F G.f.: x*(32 - x + 10*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=3
%e ..2....1....1....1....2....3....1....0....0....0....2....2....1....1....2....3
%e ..3....3....3....3....0....0....0....2....0....0....0....2....3....1....0....3
%e ..0....3....0....0....0....1....3....2....2....3....0....0....1....2....3....2
%e ..3....1....2....3....3....1....3....0....0....0....0....2....2....1....3....3
%e ..0....2....0....2....0....0....1....0....2....0....0....0....2....3....0....2
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 23 2011
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