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A200789 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases.

%I A200789 #15 Oct 21 2017 21:51:54
%S A200789 128,1791,11704,50775,169884,474566,1160616,2562633,5217520,9944957,
%T A200789 17946864,30927871,51238812,82045260,127523120,193083297,285627456,
%U A200789 413836891,588496520,822856023,1133030140,1538440146,2062298520
%N A200789 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases.
%C A200789 Row 5 of A200785.
%H A200789 R. H. Hardin, <a href="/A200789/b200789.txt">Table of n, a(n) for n = 1..137</a>
%F A200789 Empirical: a(n) = (2017/5040)*n^7 + (1427/360)*n^6 + (5759/360)*n^5 + (607/18)*n^4 + (28459/720)*n^3 + (9113/360)*n^2 + (848/105)*n + 1.
%F A200789 Conjectures from _Colin Barker_, Oct 15 2017: (Start)
%F A200789 The formulas below are consistent with the conjectured formula above.
%F A200789 G.f.: x*(128 + 767*x + 960*x^2 + 123*x^3 + 60*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A200789 a(n) = (5040 + 40704*n + 127582*n^2 + 199213*n^3 + 169960*n^4 + 80626*n^5 + 19978*n^6 + 2017*n^7) / 5040.
%F A200789 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 A200789 (End)
%e A200789 Some solutions for n=3
%e A200789 ..1....0....2....0....0....3....0....1....0....2....2....2....0....3....1....0
%e A200789 ..2....2....3....0....2....3....3....1....3....2....0....2....2....1....3....3
%e A200789 ..0....0....3....1....2....2....0....0....2....0....0....2....0....1....3....2
%e A200789 ..1....1....0....1....3....1....1....0....3....2....3....0....0....0....2....1
%e A200789 ..0....1....3....0....1....3....0....0....1....1....2....3....2....3....0....0
%e A200789 ..1....3....0....0....1....3....0....1....1....3....3....2....2....0....2....0
%e A200789 ..1....1....0....2....1....1....0....0....3....0....0....2....0....2....1....3
%K A200789 nonn
%O A200789 1,1
%A A200789 _R. H. Hardin_, Nov 22 2011