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T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with every 2 X 3 or 3 X 2 subblock having an unequal number of clockwise and counterclockwise edge increases.
9

%I #7 Oct 06 2015 21:41:26

%S 256,2208,2208,20800,37408,20800,184416,643968,643968,184416,1714176,

%T 11074704,22773384,11074704,1714176,15376544,190505040,748331168,

%U 748331168,190505040,15376544,141647296,3276916896,26462419832

%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with every 2 X 3 or 3 X 2 subblock having an unequal number of clockwise and counterclockwise edge increases.

%C Table starts

%C ........256.........2208............20800............184416...........1714176

%C .......2208........37408...........643968..........11074704.........190505040

%C ......20800.......643968.........22773384.........748331168.......26462419832

%C .....184416.....11074704........748331168.......51169273632.....3518595143968

%C ....1714176....190505040......26462419832.....3518595143968...507960770486000

%C ...15376544...3276916896.....873499447968...242220624640736.68409320823594368

%C ..141647296..56368726448...30836924266632.16680713033508736

%C .1279043040.969636795792.1019966379785120

%H R. H. Hardin, <a href="/A207799/b207799.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=4, k=3:

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 20 2012