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%I #4 Nov 23 2014 17:44:07
%S 19683,373248,373248,6859000,17318918,6859000,120553784,772693886,
%T 772693886,120553784,1990865512,32602562806,83130231052,32602562806,
%U 1990865512,32248529487,1275994883882,8367484120632,8367484120632
%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with nondecreasing maximum of every three consecutive values in every row and column
%C Table starts
%C .........19683............373248...............6859000...............120553784
%C ........373248..........17318918.............772693886.............32602562806
%C .......6859000.........772693886...........83130231052...........8367484120632
%C .....120553784.......32602562806.........8367484120632........1989073833819266
%C ....1990865512.....1275994883882.......771060995856122......427623692376852816
%C ...32248529487....48782075567391.....69143106141467242....89158016669061445146
%C ..512192024001..1821064698359512...6029492985617772723.18010964448339431996059
%C .7998800059999.66622768121582144.513483970207350870058
%H R. H. Hardin, <a href="/A250459/b250459.txt">Table of n, a(n) for n = 1..59</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 83]
%e Some solutions for n=1 k=4
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..0..0..1..2..0..1....0..0..1..0..2..1....0..0..0..0..0..1....0..0..2..2..0..2
%e ..2..0..1..2..2..0....2..0..1..2..0..1....1..0..2..2..1..2....0..1..2..2..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 23 2014