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Number of length n+3 0..5 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms
1

%I #4 Nov 04 2014 07:05:15

%S 366,966,2524,6172,13666,32500,80360,198164,474302,1140694,2782978,

%T 6829394,16652268,40525818,98972744,242571962,594328514,1454961448,

%U 3564476384,8746203338,21475833432,52737244176,129543959312,318439317418

%N Number of length n+3 0..5 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms

%C Column 5 of A249707

%H R. H. Hardin, <a href="/A249704/b249704.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +45*a(n-4) -80*a(n-5) +35*a(n-6) -757*a(n-8) +513*a(n-9) +28*a(n-10) +28*a(n-11) +6071*a(n-12) +1434*a(n-13) +314*a(n-14) -486*a(n-15) -26788*a(n-16) -25212*a(n-17) -13792*a(n-18) -4416*a(n-19) +68776*a(n-20) +102232*a(n-21) +67200*a(n-22) +29760*a(n-23) -93984*a(n-24) -186624*a(n-25) -130176*a(n-26) -43776*a(n-27) +69120*a(n-28) +138240*a(n-29) +69120*a(n-30)

%e Some solutions for n=6

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

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 04 2014