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A268073 T(n,k)=Number of nXk 0..3 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 A268073 #4 Jan 25 2016 21:12:16
%S A268073 1,2,2,4,15,4,12,159,159,12,39,2191,7445,2191,39,138,30295,381958,
%T A268073 381958,30295,138,499,421471,18691624,70985206,18691624,421471,499,
%U A268073 1830,5797959,911680225,12341773443,12341773443,911680225,5797959,1830,6723,79367143
%N A268073 T(n,k)=Number of nXk 0..3 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 A268073 Table starts
%C A268073 ....1........2.............4..............12...............39..............138
%C A268073 ....2.......15...........159............2191............30295...........421471
%C A268073 ....4......159..........7445..........381958.........18691624........911680225
%C A268073 ...12.....2191........381958........70985206......12341773443....2135811945390
%C A268073 ...39....30295......18691624.....12341773443....7496016439865.4526538615127374
%C A268073 ..138...421471.....911680225...2135811945390.4526538615127374
%C A268073 ..499..5797959...43653230106.360625109847257
%C A268073 .1830.79367143.2074179818184
%H A268073 R. H. Hardin, <a href="/A268073/b268073.txt">Table of n, a(n) for n = 1..60</a>
%F A268073 Empirical for column k:
%F A268073 k=1: a(n) = 6*a(n-1) -3*a(n-2) -30*a(n-3) +28*a(n-4) +36*a(n-5) -36*a(n-6) for n>8
%F A268073 k=2: [order 11] for n>13
%F A268073 k=3: [order 75]
%e A268073 Some solutions for n=3 k=4
%e A268073 ..0..0..1..0....0..1..1..2....0..0..1..2....0..1..1..0....0..0..1..2
%e A268073 ..0..1..2..2....0..1..2..3....0..1..0..3....0..2..1..1....0..3..0..1
%e A268073 ..3..1..1..2....1..3..2..0....3..1..0..1....2..2..0..1....2..2..1..2
%Y A268073 Column 3 is A268007.
%K A268073 nonn,tabl
%O A268073 1,2
%A A268073 _R. H. Hardin_, Jan 25 2016