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A200874 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors or less than both neighbors.

%I A200874 #10 Oct 16 2017 10:07:15
%S A200874 26,163,602,1673,3886,7973,14932,26073,43066,67991,103390,152321,
%T A200874 218414,305929,419816,565777,750330,980875,1265762,1614361,2037134,
%U A200874 2545709,3152956,3873065,4721626,5715711,6873958,8216657,9765838,11545361
%N A200874 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors or less than both neighbors.
%C A200874 Row 4 of A200871.
%H A200874 R. H. Hardin, <a href="/A200874/b200874.txt">Table of n, a(n) for n = 1..210</a>
%F A200874 Empirical: a(n) = (1/360)*n^6 + (7/24)*n^5 + (197/72)*n^4 + (185/24)*n^3 + (1667/180)*n^2 + 5*n + 1.
%F A200874 Conjectures from _Colin Barker_, Oct 16 2017: (Start)
%F A200874 G.f.: x*(26 - 19*x + 7*x^2 - 28*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A200874 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A200874 (End)
%e A200874 Some solutions for n=3
%e A200874 ..2....0....2....0....2....1....2....0....3....0....0....1....3....3....1....1
%e A200874 ..0....2....2....3....0....2....1....1....3....2....0....1....3....0....2....3
%e A200874 ..0....2....2....3....0....2....1....3....0....3....1....1....2....0....2....3
%e A200874 ..0....0....2....2....0....2....2....3....0....3....2....0....2....1....2....2
%e A200874 ..0....0....1....2....1....1....2....0....2....3....2....0....3....1....2....2
%e A200874 ..0....3....1....3....1....0....1....0....2....1....0....0....3....3....2....0
%K A200874 nonn
%O A200874 1,1
%A A200874 _R. H. Hardin_, Nov 23 2011