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A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases.

%I A200843 #9 Oct 14 2017 10:46:18
%S A200843 256,4057,28610,132263,469116,1384813,3570086,8291391,17720746,
%T A200843 35389651,66794740,120185585,207567842,345957699,558926356,878476037,
%U A200843 1347291804,2021416213,2973396622,4295957731,6106254704,8550764993,11810879754
%N A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases.
%C A200843 Row 6 of A200838.
%H A200843 R. H. Hardin, <a href="/A200843/b200843.txt">Table of n, a(n) for n = 1..210</a>
%F A200843 Empirical: a(n) = (277/4032)*n^8 + (1375/1008)*n^7 + (4933/480)*n^6 + (2723/72)*n^5 + (14161/192)*n^4 + (11197/144)*n^3 + (216211/5040)*n^2 + (929/84)*n + 1.
%F A200843 Conjectures from _Colin Barker_, Oct 14 2017: (Start)
%F A200843 G.f.: x*(256 + 1753*x + 1313*x^2 - 679*x^3 + 177*x^4 - 77*x^5 + 35*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F A200843 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 A200843 (End)
%e A200843 Some solutions for n=3
%e A200843 ..1....1....1....3....0....0....0....0....0....0....0....2....0....3....0....3
%e A200843 ..3....1....1....2....3....3....1....1....0....0....2....1....2....2....0....3
%e A200843 ..3....0....3....2....2....0....0....1....3....3....2....3....2....2....0....0
%e A200843 ..3....1....0....1....3....2....0....3....1....0....0....3....2....1....1....1
%e A200843 ..0....0....1....1....3....0....3....0....3....3....2....0....3....1....0....0
%e A200843 ..3....3....1....1....2....3....0....2....0....2....0....2....3....3....2....3
%e A200843 ..3....2....3....2....2....2....2....1....0....2....2....1....3....1....1....1
%e A200843 ..2....3....2....0....0....2....0....3....2....3....1....2....3....3....3....2
%K A200843 nonn
%O A200843 1,1
%A A200843 _R. H. Hardin_ Nov 23 2011