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%I #12 Oct 15 2017 20:28:24
%S 256,5157,43681,232275,919413,2964416,8216484,20273247,45611500,
%T 95196145,186686721,347374261,617994573,1057577400,1749504272,
%U 2808961221,4391985888,6706321909,10024306825,14698033119,21177035341,30028769640
%N Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases.
%C Row 6 of A200785.
%H R. H. Hardin, <a href="/A200790/b200790.txt">Table of n, a(n) for n = 1..136</a>
%F Empirical: a(n) = (6679/20160)*n^8 + (4799/1260)*n^7 + (26449/1440)*n^6 + (2162/45)*n^5 + (212153/2880)*n^4 + (6019/90)*n^3 + (174571/5040)*n^2 + (3893/420)*n + 1.
%F Conjectures from _Colin Barker_, Oct 15 2017: (Start)
%F G.f.: x*(256 + 2853*x + 6484*x^2 + 3294*x^3 + 522*x^4 - 79*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=3
%e ..3....1....2....2....0....2....1....2....2....3....0....0....0....3....3....1
%e ..0....1....0....2....2....3....3....2....1....3....0....1....1....0....0....3
%e ..0....3....3....1....0....1....3....1....2....0....3....0....1....0....3....1
%e ..1....3....2....2....3....3....2....2....0....2....0....0....1....3....3....2
%e ..0....1....3....2....1....3....3....1....0....1....2....3....3....1....0....0
%e ..3....0....2....2....3....0....3....3....3....3....1....2....0....2....0....3
%e ..0....1....1....2....0....0....2....0....1....0....3....1....2....1....3....1
%e ..3....0....3....3....3....1....3....0....0....3....1....0....2....3....1....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 22 2011
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