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T(n,k)=Number of nXk 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order
8

%I #5 Mar 31 2012 12:37:30

%S 1,2,2,5,6,5,15,57,57,15,52,700,2025,700,52,203,10594,103373,103373,

%T 10594,203,876,183240,6262064,20611956,6262064,183240,876,4111,

%U 3412100,404495219,4474325828,4474325828,404495219,3412100,4111,20648,65953664

%N T(n,k)=Number of nXk 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order

%C Table starts

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

%C ....2........6............57...............700..................10594

%C ....5.......57..........2025............103373................6262064

%C ...15......700........103373..........20611956.............4474325828

%C ...52....10594.......6262064........4474325828..........3309942226828

%C ..203...183240.....404495219......991613495404.......2462887498725440

%C ..876..3412100...26715084257...220845828478730....1834383283218723590

%C .4111.65953664.1777603386801.49242046909442868.1366486932112899379170

%H R. H. Hardin, <a href="/A209744/b209744.txt">Table of n, a(n) for n = 1..112</a>

%e Some solutions for n=5 k=3

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

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

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

%e ..1..2..0....0..1..2....1..2..3....2..1..2....1..3..4....0..3..4....1..2..0

%e ..3..1..0....0..3..1....0..0..0....1..0..0....1..5..3....0..5..4....1..0..3

%Y Column 1 is A056273

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 12 2012