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Number of length 5+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 #8 Aug 18 2017 09:16:07

%S 10,1189,30080,337396,2307418,11342301,44075760,143723664,409195002,

%T 1045765501,2447657872,5325777236,10897117738,21155986693,39251185824,

%U 69997645248,120555724842,201316479477,327036629344,518272784212

%N Number of length 5+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 5 of A249844.

%H R. H. Hardin, <a href="/A249849/b249849.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^9 + (4/105)*n^8 + (859/210)*n^7 + (161/180)*n^6 + (37/30)*n^5 + (313/90)*n^4 - (7/5)*n^3 + (743/1260)*n^2 + (8/105)*n.

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

%F G.f.: x*(10 + 1089*x + 18640*x^2 + 88901*x^3 + 146478*x^4 + 88511*x^5 + 18312*x^6 + 939*x^7) / (1 - x)^10.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

%F (End)

%e Some solutions for n=3

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

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014