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Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors or less than both neighbors.
1

%I #10 Oct 16 2017 10:07:15

%S 26,163,602,1673,3886,7973,14932,26073,43066,67991,103390,152321,

%T 218414,305929,419816,565777,750330,980875,1265762,1614361,2037134,

%U 2545709,3152956,3873065,4721626,5715711,6873958,8216657,9765838,11545361

%N 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 Row 4 of A200871.

%H R. H. Hardin, <a href="/A200874/b200874.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Conjectures from _Colin Barker_, Oct 16 2017: (Start)

%F G.f.: x*(26 - 19*x + 7*x^2 - 28*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.

%F 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 (End)

%e Some solutions for n=3

%e ..2....0....2....0....2....1....2....0....3....0....0....1....3....3....1....1

%e ..0....2....2....3....0....2....1....1....3....2....0....1....3....0....2....3

%e ..0....2....2....3....0....2....1....3....0....3....1....1....2....0....2....3

%e ..0....0....2....2....0....2....2....3....0....3....2....0....2....1....2....2

%e ..0....0....1....2....1....1....2....0....2....3....2....0....3....1....2....2

%e ..0....3....1....3....1....0....1....0....2....1....0....0....3....3....2....0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2011