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%I #7 Dec 10 2015 01:52:07
%S 81,270,270,972,780,972,3564,2016,2016,3564,13608,5952,4560,5952,
%T 13608,52812,17976,13344,13344,17976,52812,205416,54432,33792,48816,
%U 33792,54432,205416,803844,165936,86496,131904,131904,86496,165936,803844
%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly two counterclockwise and two clockwise edge increases.
%C Table starts
%C .....81....270....972....3564....13608.....52812.....205416......803844
%C ....270....780...2016....5952....17976.....54432.....165936......504912
%C ....972...2016...4560...13344....33792.....86496.....240192......608256
%C ...3564...5952..13344...48816...131904....444480....1645920.....4484736
%C ..13608..17976..33792..131904...516912...2156544....8613504....34039392
%C ..52812..54432..86496..444480..2156544..10584000...56633472...279244800
%C .205416.165936.240192.1645920..8613504..56633472..408445632..2199502080
%C .803844.504912.608256.4484736.34039392.279244800.2199502080.17222950080
%H R. H. Hardin, <a href="/A206094/b206094.txt">Table of n, a(n) for n = 1..839</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -a(n-2) +12*a(n-3) -36*a(n-4)
%F k=2: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -10*a(n-4) for n>6
%F k=3: a(n) = 18*a(n-3) for n>6
%F k=4: a(n) = 34*a(n-3) for n>7
%F k=5: a(n) = 66*a(n-3) for n>8
%F k=6: a(n) = 130*a(n-3) for n>9
%F k=7: a(n) = 258*a(n-3) for n>10
%F apparently a(n) = (2+2^(k+1))*a(n-3) for k>2 and n>k+3
%e Some solutions for n=4, k=3:
%e ..2..0..0..2....0..2..0..2....2..1..0..2....2..2..0..2....0..0..1..2
%e ..1..2..0..0....1..0..0..2....1..0..0..2....0..2..2..0....1..0..0..1
%e ..1..1..2..0....0..0..1..0....0..0..1..0....1..0..2..2....0..1..0..0
%e ..2..1..1..2....0..2..0..0....0..2..0..0....1..1..0..2....0..0..2..2
%e ..0..2..1..1....1..0..0..1....2..0..0..1....2..1..1..0....1..0..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 03 2012
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