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%I #4 Nov 24 2014 09:23:05
%S 512,2744,2744,13824,23096,13824,68921,181058,181058,68921,314432,
%T 1410255,2191444,1410255,314432,1367631,9788132,26447174,26447174,
%U 9788132,1367631,5832000,64023155,277462074,495646476,277462074,64023155
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with nondecreasing medians of every three consecutive values in every row and column
%C Table starts
%C .......512........2744..........13824............68921.............314432
%C ......2744.......23096.........181058..........1410255............9788132
%C .....13824......181058........2191444.........26447174..........277462074
%C .....68921.....1410255.......26447174........495646476.........7889877354
%C ....314432.....9788132......277462074.......7889877354.......186246385700
%C ...1367631....64023155.....2714800972.....116007921130......4025873039451
%C ...5832000...409593826....25923074842....1660639294043.....84585014175864
%C ..24137569..2524591167...236790657881...22580651735877...1677376060977244
%C ..97336000.15066718470..2082074710650..293919481919578..31689420451649234
%C .385828352.88100873940.17883220315081.3726137451883967.581741448021499576
%H R. H. Hardin, <a href="/A250504/b250504.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 40]
%e Some solutions for n=2 k=4
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..0..0
%e ..0..0..0..1..1..1....0..0..0..0..0..0....0..1..0..0..0..0....0..0..0..0..0..0
%e ..1..1..1..0..1..1....1..1..1..1..1..1....1..0..0..0..0..1....1..1..1..0..1..1
%e ..0..1..0..0..0..0....1..1..1..1..1..1....1..0..1..1..1..1....0..0..1..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 24 2014
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