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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
8

%I #4 Jan 10 2014 11:13:13

%S 16,58,58,208,382,208,742,2476,2476,742,2644,15936,28962,15936,2644,

%T 9418,102376,335898,335898,102376,9418,33544,657290,3886120,7017768,

%U 3886120,657290,33544,119470,4219322,44920240,146213244,146213244,44920240

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise

%C Table starts

%C ......16.........58..........208.............742...............2644

%C ......58........382.........2476...........15936.............102376

%C .....208.......2476........28962..........335898............3886120

%C .....742......15936.......335898.........7017768..........146213244

%C ....2644.....102376......3886120.......146213244.........5485253042

%C ....9418.....657290.....44920240......3043145826.......205551169550

%C ...33544....4219322....519099694.....63315473350......7699719982722

%C ..119470...27083638...5998218844...1317184566572....288383414393138

%C ..425500..173846264..69307887110..27401048899854..10800536489561114

%C .1515442.1115891712.800828757910.570010121664030.404495358726610494

%H R. H. Hardin, <a href="/A235449/b235449.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -a(n-2) -2*a(n-3)

%F k=2: a(n) = 8*a(n-1) -8*a(n-2) -16*a(n-3) +12*a(n-4) +14*a(n-5) -a(n-6) -2*a(n-7)

%F k=3: [order 19]

%F k=4: [order 53]

%e Some solutions for n=3 k=4

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

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

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

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

%Y Column 1 is A180143(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 10 2014