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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element both >= and <= some horizontal, vertical, diagonal or antidiagonal neighbor
9

%I #4 Nov 22 2013 20:22:46

%S 21,207,207,1461,5309,1461,10503,111607,111607,10503,77613,2435979,

%T 6753291,2435979,77613,575087,53921761,426813751,426813751,53921761,

%U 575087,4251717,1191667231,27382170933,78572361735,27382170933

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element both >= and <= some horizontal, vertical, diagonal or antidiagonal neighbor

%C Table starts

%C ......21.........207............1461..............10503..................77613

%C .....207........5309..........111607............2435979...............53921761

%C ....1461......111607.........6753291..........426813751............27382170933

%C ...10503.....2435979.......426813751........78572361735.........14731243506141

%C ...77613....53921761.....27382170933.....14731243506141.......8085496134786969

%C ..575087..1191667231...1753672323629...2756810145406537....4428150541972594011

%C .4251717.26307585827.112198453386465.515279597419726895.2421920880450861585787

%H R. H. Hardin, <a href="/A232352/b232352.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 8]

%F k=2: [order 23]

%F k=3: [order 80]

%e Some solutions for n=2 k=4

%e ..0..0..1..2..2....0..0..2..0..0....0..0..1..2..1....0..0..1..0..1

%e ..0..1..0..2..1....0..2..1..2..1....0..0..2..1..2....0..2..0..0..2

%e ..0..1..1..0..2....0..0..1..1..1....0..2..0..0..1....0..2..0..2..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 22 2013