%I #7 Apr 21 2021 13:48:49
%S 7,78,78,864,2520,864,9576,80496,80496,9576,106128,2574592,7380816,
%T 2574592,106128,1176192,82334080,677993552,677993552,82334080,1176192,
%U 13035456,2633043200,62266883792,178971208720,62266883792,2633043200
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.
%C Table starts
%C .........7............78...............864..................9576
%C ........78..........2520.............80496...............2574592
%C .......864.........80496...........7380816.............677993552
%C ......9576.......2574592.........677993552..........178971208720
%C ....106128......82334080.......62266883792........47230418649056
%C ...1176192....2633043200.....5718722907600.....12464482425454304
%C ..13035456...84204544256...525218223843536...3289463792785895520
%C .144468864.2692856218368.48237041019306960.868112796901730209328
%H R. H. Hardin, <a href="/A210413/b210413.txt">Table of n, a(n) for n = 1..144</a>
%e Some solutions for n=4, k=3
%e ..0..0..0..1....0..0..0..0....0..1..2..1....0..0..1..1....0..1..0..2
%e ..1..2..3..0....1..2..3..2....2..3..0..1....1..2..2..3....2..1..2..3
%e ..3..1..1..3....3..1..1..2....2..0..1..2....3..0..3..0....2..0..1..3
%e ..2..2..3..0....1..2..3..1....3..0..2..0....2..0..1..2....1..3..1..0
%e ..3..0..3..1....3..2..0..1....3..1..2..1....3..2..0..1....3..0..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 21 2012