A236155 - OEIS

%I #4 Jan 19 2014 12:28:09

%S 81,414,414,2148,2502,2148,11064,16128,16128,11064,57132,104436,

%T 146568,104436,57132,294648,676980,1351296,1351296,676980,294648,

%U 1520856,4389660,12511728,18147240,12511728,4389660,1520856,7845624,28462080

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the sets of distinct values in every 2X2 subblock

%C Table starts

%C ........81........414.........2148...........11064.............57132

%C .......414.......2502........16128..........104436............676980

%C ......2148......16128.......146568.........1351296..........12511728

%C .....11064.....104436......1351296........18147240.........244951596

%C .....57132.....676980.....12511728.......244951596........4851646302

%C ....294648....4389660....115757328......3314019456.......96273257880

%C ...1520856...28462080...1072589616.....44844204096.....1913809658142

%C ...7845624..184549536...9925448784....606910061856....38000812688892

%C ..40488216.1196622156..91969145856...8213634056940...755541000404862

%C .208893336.7758928296.851086457904.111161636064708.15002127360689268

%H R. H. Hardin, <a href="/A236155/b236155.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +18*a(n-2) +16*a(n-3) +12*a(n-4) -12*a(n-5)

%F k=2: [order 8]

%F k=3: [order 23] for n>26

%F k=4: [order 62] for n>66

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 19 2014