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%I #10 Oct 16 2017 12:23:00
%S 372,1856,9052,45648,235538,1215616,6233356,31868448,163014678,
%T 834763824,4276077566,21900661172,112149148911,574278200480,
%U 2940790043388,15059692639376,77120252989206,394927990211792,2022395235481866
%N Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.
%C Column 7 of A200886.
%H R. H. Hardin, <a href="/A200885/b200885.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) -28*a(n-2) +84*a(n-3) -126*a(n-4) +252*a(n-5) -210*a(n-6) +330*a(n-7) -165*a(n-8) +220*a(n-9) -66*a(n-10) +78*a(n-11) -13*a(n-12) +14*a(n-13) -a(n-14) +a(n-15).
%F Empirical g.f.: x*(372 - 1120*x + 4620*x^2 - 6048*x^3 + 14778*x^4 - 10800*x^5 + 20020*x^6 - 8800*x^7 + 13630*x^8 - 3600*x^9 + 4902*x^10 - 720*x^11 + 889*x^12 - 56*x^13 + 64*x^14) / (1 - 8*x + 28*x^2 - 84*x^3 + 126*x^4 - 252*x^5 + 210*x^6 - 330*x^7 + 165*x^8 - 220*x^9 + 66*x^10 - 78*x^11 + 13*x^12 - 14*x^13 + x^14 - x^15). - _Colin Barker_, Oct 16 2017
%e Some solutions for n=3
%e ..7....6....6....6....4....2....6....7....7....2....5....3....5....6....0....3
%e ..6....4....5....6....1....1....6....6....6....3....6....0....4....0....2....7
%e ..3....5....3....0....1....1....2....3....6....3....6....4....3....2....4....7
%e ..1....6....0....1....3....3....5....2....5....6....1....5....2....4....6....2
%e ..7....6....4....6....5....7....6....1....6....6....4....7....3....4....6....1
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2011
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