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%I #4 Dec 25 2013 09:51:20
%S 16584,406416,372690,9995040,24485940,8280018,245837376,1622352843,
%T 1443868938,183669567,6045322368,107611542837,254778511950,
%U 84764693441,4070647527,148657436928,7134211462374,45066201971526,39700991817357
%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with no increasing sequence of length 3 horizontally or diagonally downwards
%C Table starts
%C .......16584..........406416............9995040..............245837376
%C ......372690........24485940.........1622352843...........107611542837
%C .....8280018......1443868938.......254778511950.........45066201971526
%C ...183669567.....84764693441.....39700991817357......18662305835280147
%C ..4070647527...4966249171199...6163727050266589....7686715868506969433
%C .90202925160.290807719744802.955881551862891819.3160465819880176888222
%H R. H. Hardin, <a href="/A234380/b234380.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 19]
%F k=2: [order 55]
%F Empirical for row n:
%F n=1: a(n) = 24*a(n-1) -12*a(n-2) +624*a(n-3) +1056*a(n-4) -8448*a(n-5) -9216*a(n-6)
%F n=2: [order 23]
%F n=3: [order 58]
%e Some solutions for n=1 k=4
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..1..0..0..0..0..0....0..2..0..0..2..0....0..0..0..1..1..0....1..2..2..0..2..2
%e ..1..2..1..2..1..2....1..1..2..0..2..1....1..0..0..0..0..1....0..1..2..2..0..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 25 2013
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