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Number of (n+1)X4 0..3 arrays with every 2X2 subblock having three or four distinct values, and new values 0..3 introduced in row major order
1

%I #5 Mar 31 2012 12:37:34

%S 864,80496,7380816,677993552,62266883792,5718722907600,

%T 525218223843536,48237041019306960,4430181461077005264,

%U 406876281233712454096,37368290575302443698896,3431974791902387709770704

%N Number of (n+1)X4 0..3 arrays with every 2X2 subblock having three or four distinct values, and new values 0..3 introduced in row major order

%C Column 3 of A210413

%H R. H. Hardin, <a href="/A210408/b210408.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 81*a(n-1) +1151*a(n-2) -13041*a(n-3) -117154*a(n-4) +478740*a(n-5) +445664*a(n-6) -2873152*a(n-7) +2422784*a(n-8) -196608*a(n-9)

%e Some solutions for n=4

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 21 2012