%I #4 Jan 24 2016 09:14:31
%S 1,2,2,5,14,4,14,187,122,7,45,3552,11051,938,12,163,93311,1880990,
%T 605969,6734,20,657,3201247,555258347,982227549,30785259,45938,33,
%U 2910,137687080,256785961187,3511764501993,477324637497,1470330667,302402,54
%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column equal to the previous repeated value, and new values introduced in row-major sequential order.
%C Table starts
%C ..1.......2...........5..............14................45...............163
%C ..2......14.........187............3552.............93311...........3201247
%C ..4.....122.......11051.........1880990.........555258347......256785961187
%C ..7.....938......605969.......982227549.....3511764501993.23932385578547037
%C .12....6734....30785259....477324637497.20888913167378133
%C .20...45938..1470330667.217487430054270
%C .33..302402.67008101445
%C .54.1939154
%C .88
%H R. H. Hardin, <a href="/A268003/b268003.txt">Table of n, a(n) for n = 1..45</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-3)
%F k=2: a(n) = 14*a(n-1) -60*a(n-2) +50*a(n-3) +145*a(n-4) -80*a(n-5) -84*a(n-6) +16*a(n-7)
%F k=3: [order 20]
%e Some solutions for n=3 k=4
%e ..0..0..1..2....0..0..0..0....0..0..0..1....0..0..0..1....0..0..1..2
%e ..1..0..3..2....1..0..2..0....0..0..0..2....0..1..2..1....0..3..0..1
%e ..4..4..3..4....3..4..3..1....3..4..2..0....3..2..2..3....2..3..2..0
%Y Column 1 is A000071(n+2).
%Y Column 2 is A267906.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 24 2016