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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..2 introduced in row major order
14

%I #9 Apr 20 2013 08:17:44

%S 14,50,72,194,306,396,770,1512,2052,2160,3074,8004,13068,13800,11808,

%T 12290,43248,94116,113592,92934,64512,49154,235464,708300,1103436,

%U 992088,625512,352512,196610,1284960,5439324,11438856,13072068,8636544,4211904

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..2 introduced in row major order

%C Table starts

%C ......14.......50.......194.........770.........3074..........12290

%C ......72......306......1512........8004........43248.........235464

%C .....396.....2052.....13068.......94116.......708300........5439324

%C ....2160....13800....113592.....1103436.....11438856......122380932

%C ...11808....92934....992088....13072068....188139156.....2832970656

%C ...64512...625512...8636544...153531936...3042034560....63787803360

%C ..352512..4211904..75419136..1819019544..50032728864..1476599815224

%C .1926144.28351440.656729088.21373648800.809272164864.33256412762112

%H R. H. Hardin, <a href="/A205626/b205626.txt">Table of n, a(n) for n = 1..127</a>

%e Some solutions for n=4 k=3

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

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

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

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

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

%Y Column 1 is A205328.

%Y Row 1 is A205354.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 29 2012