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%I #5 Jan 16 2014 14:01:29
%S 40,112,112,352,232,352,1216,568,568,1216,4480,1624,1096,1624,4480,
%T 17152,5272,2536,2536,5272,17152,67072,18712,6952,4744,6952,18712,
%U 67072,265216,70168,21928,10696,10696,21928,70168,265216,1054720,271384,76456,28744
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
%C Table starts
%C ......40.....112.....352....1216....4480...17152...67072..265216..1054720
%C .....112.....232.....568....1624....5272...18712...70168..271384..1067032
%C .....352.....568....1096....2536....6952...21928...76456..283816..1091752
%C ....1216....1624....2536....4744...10696...28744...89416..309064..1141576
%C ....4480....5272....6952...10696...19720...43912..116872..361096..1242760
%C ...17152...18712...21928...28744...43912...80392..177928..471304..1451272
%C ...67072...70168...76456...89416..116872..177928..324616..716296..1892872
%C ..265216..271384..283816..309064..361096..471304..716296.1304584..2874376
%C .1054720.1067032.1091752.1141576.1242760.1451272.1892872.2874376..5230600
%C .4206592.4231192.4280488.4379464.4578952.4984072.5818888.7586824.11515912
%H R. H. Hardin, <a href="/A235893/b235893.txt">Table of n, a(n) for n = 1..309</a>
%F Empirical for diagonal and column k (the k=2..7 recurrence also works for k=1; apparently all rows and columns satisfy the same order 3 recurrence):
%F diagonal: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%F k=1: a(n) = 6*a(n-1) -8*a(n-2)
%F k=2..7..(?): a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%e Some solutions for n=4 k=4
%e ..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
%e ..1..3..1..3..1....1..1..1..2..2....3..1..3..1..3....0..3..0..2..3
%e ..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
%e ..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
%e ..1..3..1..3..1....2..2..2..1..1....3..1..3..1..3....0..3..0..2..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 16 2014