%I #4 Jan 28 2016 07:35:37
%S 1,2,2,5,14,3,14,187,96,5,45,3552,9054,726,7,163,93311,1589578,494098,
%T 5046,11,657,3201247,479973420,829256141,25770278,35574,15,2910,
%U 137687080,225814538887,3038628153922,423155007379,1339895662,242406,23
%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row equal to, and in every column unequal 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 ..3......96........9054.........1589578.........479973420......225814538887
%C ..5.....726......494098.......829256141.....3038628153922.21090319968167260
%C ..7....5046....25770278....423155007379.19146833412153174
%C .11...35574..1339895662.214576839826736
%C .15..242406.68390077014
%C .23.1653750
%C .31
%H R. H. Hardin, <a href="/A268180/b268180.txt">Table of n, a(n) for n = 1..45</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F k=2: [order 6] for n>8
%F k=3: [order 17] for n>19
%e Some solutions for n=3 k=4
%e ..0..1..2..2....0..1..0..0....0..1..1..2....0..0..1..0....0..0..0..1
%e ..0..0..3..1....0..1..0..0....0..0..1..3....0..1..2..2....0..0..1..0
%e ..3..3..1..4....1..2..3..3....4..1..0..4....3..1..2..4....2..1..3..4
%Y Column 1 is A052955(n-1).
%Y Column 2 is A267913.
%Y Row 1 is A268004.
%Y Row 2 is A268005.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 28 2016