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A268103 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column greater than or equal to the previous repeated value.

%I A268103 #4 Jan 26 2016 12:18:53
%S A268103 2,9,4,64,81,8,615,4096,729,15,7536,378225,262144,6084,28,112476,
%T A268103 56791296,232608375,15625000,49284,51,1981512,12650850576,
%U A268103 427979206656,134114290153,895841344,386884,92,40265487,3926389806144
%N A268103 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
%C A268103 Table starts
%C A268103 ..2.....9........64............615.................7536................112476
%C A268103 ..4....81......4096.........378225.............56791296...........12650850576
%C A268103 ..8...729....262144......232608375.........427979206656......1422917069386176
%C A268103 .15..6084..15625000...134114290153.....3042807800530752.151823094341278467866
%C A268103 .28.49284.895841344.74223748225767.20777755411841736998
%H A268103 R. H. Hardin, <a href="/A268103/b268103.txt">Table of n, a(n) for n = 1..48</a>
%F A268103 Empirical for column k:
%F A268103 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A268103 k=2: [order 15]
%F A268103 k=3: [order 40]
%e A268103 Some solutions for n=5 k=4
%e A268103 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A268103 ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1
%e A268103 ..0..0..0..1....0..0..0..1....0..0..0..2....0..0..0..3....0..0..0..0
%e A268103 ..0..0..0..0....0..0..3..0....0..0..0..4....0..0..1..0....0..0..1..3
%e A268103 ..1..1..1..1....0..1..0..4....4..0..1..4....3..4..0..1....4..1..0..4
%Y A268103 Column 1 is A029907(n+1).
%Y A268103 Column 2 is A268014.
%Y A268103 Column 3 is A267994.
%K A268103 nonn,tabl
%O A268103 1,1
%A A268103 _R. H. Hardin_, Jan 26 2016