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%I #4 Jan 24 2016 09:26:56
%S 1,2,2,4,14,3,12,159,96,5,40,3183,7445,726,7,154,88243,1396408,381958,
%T 5046,11,656,3222467,454238345,700411548,18691624,35574,15,3074,
%U 147078491,231327070236,2833253114538,342829793123,911680225,242406,23
%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.
%C Table starts
%C ..1.......2...........4..............12................40...............154
%C ..2......14.........159............3183.............88243...........3222467
%C ..3......96........7445.........1396408.........454238345......231327070236
%C ..5.....726......381958.......700411548.....2833253114538.21815272076639694
%C ..7....5046....18691624....342829793123.17551555370610669
%C .11...35574...911680225.166704329683286
%C .15..242406.43653230106
%C .23.1653750
%C .31
%H R. H. Hardin, <a href="/A268009/b268009.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 75]
%e Some solutions for n=3 k=4
%e ..0..0..1..1....0..1..0..0....0..0..1..1....0..0..1..1....0..0..1..2
%e ..1..1..0..2....0..0..1..1....1..2..1..2....1..1..2..2....1..2..1..3
%e ..3..1..3..1....2..0..0..2....3..4..4..3....1..2..0..1....4..2..4..4
%Y Column 1 is A052955(n-1).
%Y Column 2 is A267913.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 24 2016
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