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%I #4 Jan 19 2014 06:25:13
%S 81,576,576,3992,9979,3992,26088,169680,169680,26088,167892,2634205,
%T 7147799,2634205,167892,1060410,40097396,271135379,271135379,40097396,
%U 1060410,6648825,587963980,10003171144,25485868729,10003171144,587963980
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C .........81...........576............3992.............26088.............167892
%C ........576..........9979..........169680...........2634205...........40097396
%C .......3992........169680.........7147799.........271135379........10003171144
%C ......26088.......2634205.......271135379.......25485868729......2353737191047
%C .....167892......40097396.....10003171144.....2353737191047....558542932337300
%C ....1060410.....587963980....349054240169...204552132539376.126138961904040570
%C ....6648825....8523145663..11883153992874.17233100445331692
%C ...41411637..121700475056.392842405587563
%C ..257111073.1728432778182
%C .1592383950
%H R. H. Hardin, <a href="/A236082/b236082.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 12]
%F k=2: [order 82]
%e Some solutions for n=2 k=4
%e ..0..0..0..2..1....0..0..0..1..0....1..0..1..0..2....0..0..0..1..0
%e ..0..0..2..2..1....0..0..1..0..2....0..0..2..0..1....0..0..1..0..1
%e ..2..0..2..1..2....0..1..1..0..2....0..2..2..2..2....1..1..1..1..2
%Y Column 1 is A235737
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 19 2014