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%I #8 Oct 14 2017 10:46:01
%S 176,846,4108,19930,96690,469116,2276028,11042700,53576350,259938722,
%T 1261156090,6118806300,29686880836,144033141554,698811908924,
%U 3390456382404,16449625906804,79809371351400,387214626739458
%N Number of 0..5 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
%C Column 5 of A200838.
%H R. H. Hardin, <a href="/A200835/b200835.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) -6*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7).
%F Empirical g.f.: 2*x*(88 - 105*x + 44*x^2 - 85*x^3 + 50*x^4 - 33*x^5 + 18*x^6) / (1 - 6*x + 6*x^2 - 3*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7). - _Colin Barker_, Oct 14 2017
%e Some solutions for n=3
%e ..3....5....0....4....2....3....2....5....3....1....2....0....0....4....1....3
%e ..3....4....3....1....1....5....0....1....0....1....3....5....2....5....4....4
%e ..0....4....0....1....5....3....4....2....5....1....3....4....1....0....4....0
%e ..0....0....2....4....0....3....2....2....4....3....1....5....1....4....4....0
%e ..1....1....1....2....0....5....3....2....4....3....1....5....2....0....0....5
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 23 2011
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