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%I #7 May 09 2014 00:04:43
%S 15,132,132,1571,3798,1571,18995,112194,112194,18995,230395,3315908,
%T 8080990,3315908,230395,2794651,97991800,582449912,582449912,97991800,
%U 2794651,33899863,2895999006,41971475967,102557201298,41971475967
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays colored with the sets of distinct values in every 2 X 2 subblock, with new values 0..3 introduced row-major order.
%C Table starts:
%C ........15.........132..........1571..........18995.........230395
%C .......132........3798........112194........3315908.......97991800
%C ......1571......112194.......8080990......582449912....41971475967
%C .....18995.....3315908.....582449912...102557201298.18043516803602
%C ....230395....97991800...41971475967.18043516803602
%C ...2794651..2895999006.3024814165927
%C ..33899863.85585437564
%C .411212991
%H R. H. Hardin, <a href="/A236262/b236262.txt">Table of n, a(n) for n = 1..40</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 8] for n>9.
%F k=2: [order 21] for n>23.
%e Some solutions for n=2, k=4:
%e ..0..0..1..2..2....0..0..1..0..0....0..0..1..2..1....0..0..1..1..2
%e ..0..3..3..0..0....0..2..1..0..3....0..2..1..2..3....0..0..0..3..3
%e ..0..1..2..0..3....0..1..2..3..2....1..2..2..0..3....1..2..2..3..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 21 2014