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A249848 Number of length 4+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 18:10:59

%S 10,653,11052,92190,499654,2029683,6712760,19039308,47942370,

%T 109802473,232780196,462822282,871727454,1567698415,2708846832,

%U 4520158424,7314465594,11518015365,17701260700,26615543606,39236378742,56814086571

%N Number of length 4+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 4 of A249844.

%H R. H. Hardin, <a href="/A249848/b249848.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^8 + (13/21)*n^7 + (101/30)*n^6 + (71/30)*n^5 + (2/3)*n^4 + 2*n^3 - (1/30)*n^2 + (1/70)*n.

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

%F G.f.: x*(10 + 563*x + 5535*x^2 + 15390*x^3 + 14224*x^4 + 4287*x^5 + 311*x^6) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=4

%e ..0....2....0....4....3....3....2....0....3....2....3....4....0....0....2....4

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

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

%e ..0....4....0....3....4....0....0....3....4....0....0....0....0....0....0....4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014

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Last modified March 29 02:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)