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%I #10 Oct 16 2017 10:06:48
%S 110,1523,9858,42479,141688,395929,971416,2156867,4424298,8509105,
%T 15512938,27033149,45322876,73486107,115712352,177555837,266264422,
%U 391163735,564102306,799963779,1117252576,1538759685,2092315544
%N Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors or less than both neighbors.
%C Row 7 of A200871.
%H R. H. Hardin, <a href="/A200877/b200877.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/181440)*n^9 + (131/20160)*n^8 + (8893/30240)*n^7 + (4621/1440)*n^6 + (118933/8640)*n^5 + (83957/2880)*n^4 + (763489/22680)*n^3 + (36343/1680)*n^2 + (9169/1260)*n + 1.
%F Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F G.f.: x*(110 + 423*x - 422*x^2 - 766*x^3 + 848*x^4 - 246*x^5 + 90*x^6 - 44*x^7 + 10*x^8 - x^9) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F (End)
%e Some solutions for n=3
%e ..3....3....3....3....3....0....2....2....3....2....3....3....1....1....2....2
%e ..0....0....0....1....3....0....2....2....3....3....3....1....2....1....2....0
%e ..0....0....0....1....3....2....1....0....3....3....3....1....2....1....1....0
%e ..0....2....1....1....2....2....0....0....2....3....3....1....3....3....1....0
%e ..3....2....3....1....1....2....0....2....2....3....1....3....3....3....0....0
%e ..3....1....3....3....1....2....1....2....1....2....1....3....3....2....0....0
%e ..3....0....3....3....0....2....2....0....1....0....1....3....2....1....0....0
%e ..2....0....2....2....0....1....3....0....1....0....1....3....2....0....1....0
%e ..0....1....2....1....2....1....3....2....1....1....3....2....3....0....3....3
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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