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A268003 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.

%I A268003 #4 Jan 24 2016 09:14:31
%S A268003 1,2,2,5,14,4,14,187,122,7,45,3552,11051,938,12,163,93311,1880990,
%T A268003 605969,6734,20,657,3201247,555258347,982227549,30785259,45938,33,
%U A268003 2910,137687080,256785961187,3511764501993,477324637497,1470330667,302402,54
%N A268003 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 A268003 Table starts
%C A268003 ..1.......2...........5..............14................45...............163
%C A268003 ..2......14.........187............3552.............93311...........3201247
%C A268003 ..4.....122.......11051.........1880990.........555258347......256785961187
%C A268003 ..7.....938......605969.......982227549.....3511764501993.23932385578547037
%C A268003 .12....6734....30785259....477324637497.20888913167378133
%C A268003 .20...45938..1470330667.217487430054270
%C A268003 .33..302402.67008101445
%C A268003 .54.1939154
%C A268003 .88
%H A268003 R. H. Hardin, <a href="/A268003/b268003.txt">Table of n, a(n) for n = 1..45</a>
%F A268003 Empirical for column k:
%F A268003 k=1: a(n) = 2*a(n-1) -a(n-3)
%F A268003 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 A268003 k=3: [order 20]
%e A268003 Some solutions for n=3 k=4
%e A268003 ..0..0..1..2....0..0..0..0....0..0..0..1....0..0..0..1....0..0..1..2
%e A268003 ..1..0..3..2....1..0..2..0....0..0..0..2....0..1..2..1....0..3..0..1
%e A268003 ..4..4..3..4....3..4..3..1....3..4..2..0....3..2..2..3....2..3..2..0
%Y A268003 Column 1 is A000071(n+2).
%Y A268003 Column 2 is A267906.
%K A268003 nonn,tabl
%O A268003 1,2
%A A268003 _R. H. Hardin_, Jan 24 2016