%I #10 Oct 14 2017 10:46:09

%S 16,69,194,435,846,1491,2444,3789,5620,8041,11166,15119,20034,26055,

%T 33336,42041,52344,64429,78490,94731,113366,134619,158724,185925,

%U 216476,250641,288694,330919,377610,429071,485616,547569,615264,689045,769266

%N Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases.

%C Row 2 of A200838.

%H R. H. Hardin, <a href="/A200839/b200839.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (5/12)*n^4 + (19/6)*n^3 + (79/12)*n^2 + (29/6)*n + 1.

%F Conjectures from _Colin Barker_, Oct 14 2017: (Start)

%F G.f.: x*(16 - 11*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 ..3....3....1....1....3....2....2....2....2....0....2....0....2....3....0....1

%e ..1....1....0....1....3....2....3....0....1....0....2....1....3....3....1....2

%e ..1....1....0....3....3....0....1....0....3....2....1....0....0....1....1....2

%e ..2....3....3....1....3....3....2....1....3....0....1....0....3....1....3....0

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 23 2011