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%I #4 Jan 25 2016 10:52:56
%S 1,2,2,4,14,4,12,159,122,7,40,3183,9054,938,12,154,88243,1650058,
%T 467899,6734,20,656,3222467,525124941,829256141,22309009,45938,33,
%U 3074,147078491,262999737747,3273871468927,386602239495,999810316,302402,54
%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row unequal to, and in every column equal 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 ..4.....122........9054.........1650058.........525124941......262999737747
%C ..7.....938......467899.......829256141.....3273871468927.24754240745963975
%C .12....6734....22309009....386602239495.19146833412153174
%C .20...45938...999810316.168939588471080
%C .33..302402.42764566838
%C .54.1939154
%C .88
%H R. H. Hardin, <a href="/A268049/b268049.txt">Table of n, a(n) for n = 1..48</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-3)
%F 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 k=3: [order 78]
%e Some solutions for n=5 k=4
%e ..0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0
%e ..0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0
%e ..2..0..0..1....2..1..0..3....1..0..0..1....1..1..0..2....2..0..0..3
%e ..3..0..0..2....4..0..0..4....0..2..0..3....0..1..0..3....4..4..0..1
%e ..4..2..4..1....3..2..0..1....0..2..0..1....3..4..0..2....1..1..3..0
%Y Column 1 is A000071(n+2).
%Y Column 2 is A267906.
%Y Row 1 is A268010.
%Y Row 2 is A268011.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 25 2016
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