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A200889 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.

%I A200889 #10 Oct 16 2017 12:23:14
%S A200889 37,292,1268,3985,10213,22736,45648,84681,147565,244420,388180,595049,
%T A200889 884989,1282240,1815872,2520369,3436245,4610692,6098260,7961569,
%U A200889 10272053,13110736,16569040,20749625,25767261,31749732,38838772,47191033,56979085
%N A200889 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.
%C A200889 Row 4 of A200886.
%H A200889 R. H. Hardin, <a href="/A200889/b200889.txt">Table of n, a(n) for n = 1..210</a>
%F A200889 Empirical: a(n) = (2/45)*n^6 + (19/15)*n^5 + (217/36)*n^4 + (71/6)*n^3 + (2057/180)*n^2 + (27/5)*n + 1.
%F A200889 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200889 G.f.: x*(37 + 33*x + x^2 - 54*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A200889 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 A200889 (End)
%e A200889 Some solutions for n=3
%e A200889 ..1....0....3....0....2....2....1....0....1....3....2....3....2....2....3....2
%e A200889 ..0....1....1....3....1....3....1....0....1....0....2....3....3....1....1....2
%e A200889 ..1....2....0....3....3....3....2....0....0....1....1....0....3....0....3....2
%e A200889 ..3....2....1....0....3....2....2....1....1....2....0....0....1....0....3....2
%e A200889 ..3....2....2....0....1....2....3....2....2....2....1....2....0....2....2....1
%e A200889 ..3....3....2....3....1....0....3....2....2....1....2....2....3....3....2....0
%K A200889 nonn
%O A200889 1,1
%A A200889 _R. H. Hardin_, Nov 23 2011