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A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.

%I A200890 #9 Oct 16 2017 10:50:01
%S A200890 65,704,3823,14288,42182,105813,235538,478467,904111,1611038,2734601,
%T A200890 4455802,7011356,10705019,15920244,23134229,32933421,46030540,
%U A200890 63283187,85714100,114533122,151160945,197254694,254735415,325817531,413040330
%N A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.
%C A200890 Row 5 of A200886.
%H A200890 R. H. Hardin, <a href="/A200890/b200890.txt">Table of n, a(n) for n = 1..210</a>
%F A200890 Empirical: a(n) = (4/315)*n^7 + (7/9)*n^6 + (241/45)*n^5 + (1067/72)*n^4 + (3757/180)*n^3 + (1145/72)*n^2 + (2629/420)*n + 1.
%F A200890 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200890 G.f.: x*(65 + 184*x + 11*x^2 - 224*x^3 + 48*x^4 - 27*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A200890 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A200890 (End)
%e A200890 Some solutions for n=3
%e A200890 ..0....2....3....2....2....3....2....0....2....0....2....2....3....2....1....1
%e A200890 ..1....3....0....2....0....2....2....3....3....3....0....0....1....2....0....2
%e A200890 ..1....3....0....3....3....2....1....3....3....3....3....1....2....3....2....2
%e A200890 ..0....0....2....3....3....0....2....3....3....2....3....1....2....3....2....2
%e A200890 ..2....1....3....0....2....0....2....2....0....3....2....0....2....3....2....2
%e A200890 ..2....1....3....0....2....2....0....0....1....3....0....1....1....3....0....0
%e A200890 ..2....3....2....2....1....3....1....0....3....3....1....1....0....3....1....1
%K A200890 nonn
%O A200890 1,1
%A A200890 _R. H. Hardin_, Nov 23 2011