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%I #4 Nov 20 2013 18:55:55
%S 15,109,109,685,2129,685,4483,39651,39651,4483,29469,745157,2064527,
%T 745157,29469,193531,14015499,108997581,108997581,14015499,193531,
%U 1270657,263553379,5765893981,16237318767,5765893981,263553379,1270657
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element both >= and <= some horizontal, vertical or antidiagonal neighbor
%C Table starts
%C ......15........109............685..............4483.................29469
%C .....109.......2129..........39651............745157..............14015499
%C .....685......39651........2064527.........108997581............5765893981
%C ....4483.....745157......108997581.......16237318767.........2425888162725
%C ...29469...14015499.....5765893981.....2425888162725......1024215443152687
%C ..193531..263553379...304936615565...362285582855051....432206209011195289
%C .1270657.4955798535.16125727718291.54098452658673021.182361235082538718699
%H R. H. Hardin, <a href="/A232204/b232204.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 12]
%F k=2: [order 38] for n>40
%e Some solutions for n=2 k=4
%e ..0..1..1..0..0....0..0..2..2..2....0..1..0..2..2....0..0..2..2..2
%e ..0..2..0..0..1....0..2..2..0..0....0..1..0..0..1....0..1..1..2..1
%e ..0..2..1..0..1....1..2..2..2..2....0..0..0..1..1....0..0..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 20 2013
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