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%I #4 Jan 03 2015 09:11:11
%S 81,459,459,1963,2722,1963,7253,9255,9255,7253,25165,27070,22418,
%T 27070,25165,85663,71333,62237,62237,71333,85663,291511,176266,142679,
%U 182493,142679,176266,291511,997121,416901,327147,398710,398710,327147,416901
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically
%C Table starts
%C .......81.....459....1963.....7253....25165....85663....291511....997121
%C ......459....2722....9255....27070....71333...176266....416901....955594
%C .....1963....9255...22418....62237...142679...327147....700492...1477077
%C .....7253...27070...62237...182493...398710...949158...2008246...4342893
%C ....25165...71333..142679...398710...745281..1744459...3362641...7208222
%C ....85663..176266..327147...949158..1744459..4292539...8304638..18590483
%C ...291511..416901..700492..2008246..3362641..8304638..14461240..32033588
%C ...997121..955594.1477077..4342893..7208222.18590483..32033588..74067255
%C ..3427953.2141571.3032758..8951319.14186738.37412196..59607552.139286102
%C .11826315.4715371.6133637.18483480.29111786.79632497.124813784.303938928
%H R. H. Hardin, <a href="/A253533/b253533.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 8]
%F k=2: [order 17] for n>27
%F k=3: [order 20] for n>29
%F k=4: [order 18] for n>31
%F k=5: [order 23] for n>40
%F k=6: [order 21] for n>42
%F k=7: [order 27] for n>52
%e Some solutions for n=4 k=4
%e ..1..1..1..2..1....1..1..0..1..1....1..0..0..1..2....1..1..0..1..2
%e ..1..1..0..1..0....0..1..0..1..0....2..1..0..1..1....1..1..0..1..1
%e ..0..1..0..1..0....0..1..0..1..0....2..2..1..2..1....2..2..1..2..2
%e ..0..1..0..2..1....0..1..0..1..0....1..1..0..1..0....1..1..0..1..1
%e ..0..1..0..2..0....0..1..0..2..1....0..1..1..2..1....0..1..0..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 03 2015
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