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A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases.

%I A200842 #9 Oct 15 2017 01:11:54
%S A200842 128,1465,8210,31677,96690,250913,577660,1212729,2365804,4346969,
%T A200842 7598878,12735125,20585358,32247681,49148888,73113073,106439160,
%U A200842 151987897,213278858,294597997,401116298,539020065,715653396,939673385,1221218596
%N A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases.
%C A200842 Row 5 of A200838.
%H A200842 R. H. Hardin, <a href="/A200842/b200842.txt">Table of n, a(n) for n = 1..210</a>
%F A200842 Empirical: a(n) = (34/315)*n^7 + (163/90)*n^6 + (1981/180)*n^5 + (557/18)*n^4 + (7807/180)*n^3 + (1361/45)*n^2 + (333/35)*n + 1.
%F A200842 Conjectures from _Colin Barker_, Oct 14 2017: (Start)
%F A200842 G.f.: x*(128 + 441*x + 74*x^2 - 151*x^3 + 74*x^4 - 29*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A200842 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 A200842 (End)
%e A200842 Some solutions for n=3
%e A200842 ..3....2....2....0....0....2....1....2....3....1....2....0....2....3....3....0
%e A200842 ..1....1....2....1....1....1....0....0....3....1....0....3....0....3....0....2
%e A200842 ..1....1....0....1....1....2....3....1....0....0....0....2....0....3....2....1
%e A200842 ..1....2....0....0....1....0....0....0....2....1....3....2....0....2....0....2
%e A200842 ..3....1....3....0....1....0....2....3....1....0....2....1....3....2....1....2
%e A200842 ..1....1....3....0....3....3....1....3....2....0....3....3....1....0....1....2
%e A200842 ..1....0....3....3....2....0....1....1....2....2....2....1....1....2....3....3
%K A200842 nonn
%O A200842 1,1
%A A200842 _R. H. Hardin_ Nov 23 2011