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%I #4 Nov 23 2013 13:39:56
%S 15,159,109,973,2689,611,6477,44971,48971,3635,46713,876881,2189991,
%T 890283,21717,334521,18073053,119994763,107913855,16262989,129323,
%U 2375879,366033741,7049296087,16776955943,5322933313,296516955,770747
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element both >= and <= some horizontal, diagonal or antidiagonal neighbor
%C Table starts
%C .....15........159............973..............6477.................46713
%C ....109.......2689..........44971............876881..............18073053
%C ....611......48971........2189991.........119994763............7049296087
%C ...3635.....890283......107913855.......16776955943.........2832909399671
%C ..21717...16262989.....5322933313.....2346397695011......1137726954093673
%C .129323..296516955...262249675165...327861770666547....456432801562470697
%C .770747.5408696699.12924602609687.45820119635323263.183153958944323007479
%H R. H. Hardin, <a href="/A232414/b232414.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 9]
%F k=2: [order 14]
%F k=3: [order 64]
%F Empirical for row n:
%F n=1: [linear recurrence of order 10]
%F n=2: [order 34]
%e Some solutions for n=2 k=4
%e ..0..0..1..2..1....0..0..0..1..1....0..0..1..1..2....0..0..1..1..1
%e ..0..2..2..1..1....0..2..2..2..1....0..0..2..2..2....0..1..2..1..1
%e ..2..0..1..1..1....2..1..1..1..2....0..1..0..2..2....1..2..2..1..1
%Y Column 1 is A232117
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 23 2013