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A268009 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.

%I A268009 #4 Jan 24 2016 09:26:56
%S A268009 1,2,2,4,14,3,12,159,96,5,40,3183,7445,726,7,154,88243,1396408,381958,
%T A268009 5046,11,656,3222467,454238345,700411548,18691624,35574,15,3074,
%U A268009 147078491,231327070236,2833253114538,342829793123,911680225,242406,23
%N A268009 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 A268009 Table starts
%C A268009 ..1.......2...........4..............12................40...............154
%C A268009 ..2......14.........159............3183.............88243...........3222467
%C A268009 ..3......96........7445.........1396408.........454238345......231327070236
%C A268009 ..5.....726......381958.......700411548.....2833253114538.21815272076639694
%C A268009 ..7....5046....18691624....342829793123.17551555370610669
%C A268009 .11...35574...911680225.166704329683286
%C A268009 .15..242406.43653230106
%C A268009 .23.1653750
%C A268009 .31
%H A268009 R. H. Hardin, <a href="/A268009/b268009.txt">Table of n, a(n) for n = 1..45</a>
%F A268009 Empirical for column k:
%F A268009 k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F A268009 k=2: [order 6] for n>8
%F A268009 k=3: [order 75]
%e A268009 Some solutions for n=3 k=4
%e A268009 ..0..0..1..1....0..1..0..0....0..0..1..1....0..0..1..1....0..0..1..2
%e A268009 ..1..1..0..2....0..0..1..1....1..2..1..2....1..1..2..2....1..2..1..3
%e A268009 ..3..1..3..1....2..0..0..2....3..4..4..3....1..2..0..1....4..2..4..4
%Y A268009 Column 1 is A052955(n-1).
%Y A268009 Column 2 is A267913.
%K A268009 nonn,tabl
%O A268009 1,2
%A A268009 _R. H. Hardin_, Jan 24 2016