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T(n,k)=Number of nXk 0..7 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..7 introduced in row major order
8

%I #5 Mar 31 2012 12:37:29

%S 1,2,2,5,6,5,15,57,57,15,52,700,2027,700,52,203,10677,107693,107693,

%T 10677,203,877,193676,7700397,27323948,7700397,193676,877,4140,

%U 4054358,687132348,9700576474,9700576474,687132348,4054358,4140,21146,95534880

%N T(n,k)=Number of nXk 0..7 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..7 introduced in row major order

%C Table starts

%C ....1........2.............5.................15.......................52

%C ....2........6............57................700....................10677

%C ....5.......57..........2027.............107693..................7700397

%C ...15......700........107693...........27323948...............9700576474

%C ...52....10677.......7700397.........9700576474...........16484968944748

%C ..203...193676.....687132348......4194606038254........31813625228165210

%C ..877..4054358...71519658191...2002617518101082.....64398780661554524050

%C .4140.95534880.8190834795146.999998646599976052.132601740316897661044124

%H R. H. Hardin, <a href="/A209527/b209527.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=5 k=3

%e ..0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..0

%e ..1..2..1....1..2..1....1..2..1....1..2..0....1..2..2....1..2..3....0..2..0

%e ..2..0..0....0..0..0....0..0..1....1..0..3....0..0..1....1..0..0....0..1..0

%e ..0..3..1....1..2..1....1..2..0....0..2..0....1..2..0....0..2..3....0..2..1

%e ..3..1..0....0..1..0....0..0..1....0..1..0....0..0..1....2..3..0....1..2..0

%Y Column 1 is A099263

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 10 2012