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%I #10 Oct 15 2017 20:28:37
%S 273,1491,8239,45465,250913,1384813,7642875,42181611,232803603,
%T 1284861277,7091249941,39137163521,216001069269,1192126810953,
%U 6579441195743,36312451033865,200411259993515,1106085433196691
%N Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
%C Column 6 of A200838.
%H R. H. Hardin, <a href="/A200836/b200836.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) -9*a(n-2) +6*a(n-3) -9*a(n-4) +7*a(n-5) -7*a(n-6) +5*a(n-7) -2*a(n-8) +a(n-9).
%F Empirical g.f.: x*(273 - 420*x + 259*x^2 - 427*x^3 + 320*x^4 - 319*x^5 + 236*x^6 - 91*x^7 + 49*x^8) / (1 - 7*x + 9*x^2 - 6*x^3 + 9*x^4 - 7*x^5 + 7*x^6 - 5*x^7 + 2*x^8 - x^9). - _Colin Barker_, Oct 15 2017
%e Some solutions for n=3
%e ..2....4....4....4....0....1....2....4....2....5....4....4....5....2....1....3
%e ..1....3....6....3....3....5....5....3....4....2....3....0....0....1....6....5
%e ..4....4....3....6....1....0....4....3....4....2....3....0....1....6....3....0
%e ..3....2....6....2....5....0....4....1....3....2....6....6....0....0....3....3
%e ..4....5....3....5....4....1....6....3....5....3....4....3....6....5....6....3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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