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%I #5 Mar 31 2012 12:37:01
%S 3570,34274,34274,423416,154938,423416,2827014,781884,781884,2827014,
%T 22956524,5597126,947990,5597126,22956524,254913953,52039032,5776350,
%U 5776350,52039032,254913953,2004465237,395943745,49914501,11785518
%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three strictly increasing elements in a row horizontally or vertically, exactly one way
%C Table starts
%C ........3570.......34274......423416.....2827014....22956524....254913953
%C .......34274......154938......781884.....5597126....52039032....395943745
%C ......423416......781884......947990.....5776350....49914501....422397021
%C .....2827014.....5597126.....5776350....11785518....89459577...1122887052
%C ....22956524....52039032....49914501....89459577...253954944...1364559057
%C ...254913953...395943745...422397021..1122887052..1364559057...2050960896
%C ..2004465237..2826265830..3619976949..6016853259..8802512928..13168291392
%C .15823989959.26252359826.29207652750.53009843553.94119917760.115434720000
%H R. H. Hardin, <a href="/A204417/b204417.txt">Table of n, a(n) for n = 1..924</a>
%F Empirical for column k:
%F k=1: (order 14 recurrence)
%F k=2: (order 19 recurrence for n>22)
%F k=3: a(n) = 577*a(n-3) +63*a(n-5) -63*a(n-8) for n>16
%F k=4: a(n) = 577*a(n-3) for n>15
%F k=5: a(n) = 577*a(n-3) for n>16
%F k=6: a(n) = 577*a(n-3) for n>17
%F k=7: a(n) = 577*a(n-3) for n>18
%e Some solutions for n=3 k=3
%e ..0..0..2..2..2....2..2..0..0..2....0..0..2..0..1....1..2..2..1..0
%e ..0..1..0..1..2....2..1..0..1..0....0..0..0..1..0....0..0..1..2..1
%e ..1..2..2..1..0....0..1..2..2..1....0..1..2..2..1....0..1..2..1..2
%e ..2..0..1..2..1....0..0..1..2..2....1..0..1..2..2....1..1..0..1..2
%e ..0..1..2..1..2....0..1..0..1..2....0..1..0..1..2....0..0..1..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 15 2012
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