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A200884 Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

%I A200884 #10 Oct 16 2017 12:22:52
%S A200884 252,1127,4977,22736,105813,491533,2269938,10462235,48259083,
%T A200884 222798408,1028746629,4749274209,21922813539,101196577809,
%U A200884 467142348798,2156444661242,9954648966159,45952741121083,212127214776309
%N A200884 Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.
%C A200884 Column 6 of A200886.
%H A200884 R. H. Hardin, <a href="/A200884/b200884.txt">Table of n, a(n) for n = 1..210</a>
%F A200884 Empirical: a(n) = 7*a(n-1) -21*a(n-2) +56*a(n-3) -70*a(n-4) +126*a(n-5) -84*a(n-6) +120*a(n-7) -45*a(n-8) +55*a(n-9) -11*a(n-10) +12*a(n-11) -a(n-12) +a(n-13).
%F A200884 Empirical g.f.: x*(252 - 637*x + 2380*x^2 - 2548*x^3 + 5706*x^4 - 3276*x^5 + 5620*x^6 - 1820*x^7 + 2630*x^8 - 455*x^9 + 582*x^10 - 42*x^11 + 49*x^12) / (1 - 7*x + 21*x^2 - 56*x^3 + 70*x^4 - 126*x^5 + 84*x^6 - 120*x^7 + 45*x^8 - 55*x^9 + 11*x^10 - 12*x^11 + x^12 - x^13). - _Colin Barker_, Oct 16 2017
%e A200884 Some solutions for n=3
%e A200884 ..6....1....2....1....1....4....0....2....2....5....3....3....4....1....4....5
%e A200884 ..6....1....2....1....3....4....1....1....5....2....3....3....0....3....0....6
%e A200884 ..5....0....5....5....4....4....2....1....5....0....2....1....2....5....1....6
%e A200884 ..2....2....5....5....4....2....4....5....0....3....2....1....3....5....6....5
%e A200884 ..6....3....6....3....1....3....4....6....5....4....5....5....6....1....6....4
%K A200884 nonn
%O A200884 1,1
%A A200884 _R. H. Hardin_, Nov 23 2011