%I #9 Oct 15 2017 01:11:48
%S 64,529,2356,7587,19930,45465,93472,177381,315844,533929,864436,
%T 1349335,2041326,3005521,4321248,6083977,8407368,11425441,15294868,
%U 20197387,26342338,33969321,43350976,54795885,68651596,85307769,105199444
%N Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases or two consecutive decreases.
%C Row 4 of A200838.
%H R. H. Hardin, <a href="/A200841/b200841.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (61/360)*n^6 + (93/40)*n^5 + (779/72)*n^4 + (521/24)*n^3 + (1801/90)*n^2 + (239/30)*n + 1.
%F Conjectures from _Colin Barker_, Oct 14 2017: (Start)
%F G.f.: x*(64 + 81*x - 3*x^2 - 36*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=3
%e ..3....0....3....3....1....2....1....1....3....3....3....1....2....0....3....1
%e ..3....3....3....3....0....3....3....1....1....0....0....0....3....3....3....1
%e ..3....0....1....3....3....3....2....0....2....0....3....1....0....2....0....1
%e ..3....2....1....1....0....0....3....0....1....3....2....1....0....3....0....3
%e ..0....0....1....1....0....0....3....0....1....3....3....0....3....1....0....3
%e ..3....3....0....3....3....3....0....0....0....2....1....0....1....1....0....2
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 23 2011