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Number of length 1+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.
1

%I #10 Aug 18 2017 11:15:42

%S 10,110,560,1920,5170,11830,24080,44880,78090,128590,202400,306800,

%T 450450,643510,897760,1226720,1645770,2172270,2825680,3627680,4602290,

%U 5775990,7177840,8839600,10795850,13084110,15744960,18822160,22362770

%N Number of length 1+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.

%C Row 1 of A249844.

%H R. H. Hardin, <a href="/A249845/b249845.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + (5/2)*n^4 + (10/3)*n^3 + (5/2)*n^2 + (2/3)*n.

%F Conjectures from _Colin Barker_, Aug 18 2017: (Start)

%F G.f.: 10*x*(1 + x)*(1 + 4*x + x^2) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=6

%e ..5....6....6....3....5....0....4....5....4....0....3....1....6....0....3....5

%e ..0....3....6....4....3....5....1....4....3....1....5....2....3....1....1....3

%e ..6....0....2....3....2....0....6....6....2....0....4....3....5....0....5....1

%e ..1....2....1....2....1....4....4....1....5....3....1....3....3....2....4....4

%e ..2....5....3....1....6....6....2....1....5....2....0....3....6....2....4....0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014