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A268180 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.

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