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%I #4 Dec 11 2013 08:22:27
%S 172952,8254896,8254896,386906152,1328621536,386906152,18116531520,
%T 208066125583,208066125583,18116531520,846914338316,32519299606118,
%U 107592918949238,32519299606118,846914338316,39587056212137
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no increasing sequence of length 3 horizontally, diagonally downwards or vertically
%C Table starts
%C .......172952..........8254896............386906152..............18116531520
%C ......8254896.......1328621536.........208066125583...........32519299606118
%C ....386906152.....208066125583......107592918949238........55442546308058920
%C ..18116531520...32519299606118....55442546308058920.....94038386779753884364
%C .846914338316.5070020645309648.28457838067515915868.158651203925316697808911
%H R. H. Hardin, <a href="/A233488/b233488.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 60]
%e Some solutions for n=1 k=4
%e ..1..1..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..2..1..0..0..0..0....2..3..0..0..0..0....2..0..0..0..0..0....2..0..0..0..0..0
%e ..2..1..3..3..1..1....2..3..2..3..2..3....0..3..2..2..0..0....2..3..1..3..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 11 2013