%I #6 Apr 11 2023 13:39:13
%S 256,2500,2500,22500,64660,22500,173056,1494029,1494029,173056,
%T 1252161,27945953,86208566,27945953,1252161,8444836,480842776,
%U 3816838692,3816838692,480842776,8444836,54700816,7521121248,152303295344
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with nondecreasing maximum of every two consecutive values in every row and column.
%C Table starts
%C ......256.........2500...........22500.............173056...............1252161
%C .....2500........64660.........1494029...........27945953.............480842776
%C ....22500......1494029........86208566.........3816838692..........152303295344
%C ...173056.....27945953......3816838692.......384534346812........34305606524366
%C ..1252161....480842776....152303295344.....34305606524366......6735269828703846
%C ..8444836...7521121248...5387348466660...2665290749762401...1132975802012504908
%C .54700816.111353209662.177938935415798.191258469961340217.174360788514275098552
%H R. H. Hardin, <a href="/A251120/b251120.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 26]
%e Some solutions for n=2, k=4
%e ..0..0..0..0..0....0..0..0..2..2....0..0..0..2..3....0..0..2..0..2
%e ..0..0..0..1..3....0..0..0..0..2....0..0..0..0..3....0..0..0..0..0
%e ..1..2..2..2..2....0..2..1..2..2....0..3..2..3..3....0..1..3..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014