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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, vertically or nw-to-se diagonally exactly one way
9

%I #5 Mar 31 2012 12:37:02

%S 3562,29678,29678,328845,144168,328845,2275645,741296,741296,2275645,

%T 16247580,4820300,981914,4820300,16247580,153711850,40672735,5260434,

%U 5260434,40672735,153711850,1240455298,304865717,43980907,10978524

%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, vertically or nw-to-se diagonally exactly one way

%C Table starts

%C .......3562.......29678......328845.....2275645....16247580...153711850

%C ......29678......144168......741296.....4820300....40672735...304865717

%C .....328845......741296......981914.....5260434....43980907...327968423

%C ....2275645.....4820300.....5260434....10978524....69792825...774393122

%C ...16247580....40672735....43980907....69792825...207096000..1139760144

%C ..153711850...304865717...327968423...774393122..1139760144..1719348416

%C .1240455298..1982068849..2572437376..4518555426..6656676736..9620299328

%C .9111381604.16593833004.19830769591.32448416953.61015724528.81184579243

%H R. H. Hardin, <a href="/A204607/b204607.txt">Table of n, a(n) for n = 1..611</a>

%F Empirical for column k:

%F k=1: (order 24 recurrence)

%F k=2: (order 30 recurrence for n>33)

%F k=3: a(n) = 442*a(n-3) +63*a(n-5) +43*a(n-6) -63*a(n-8) +81*a(n-9) -81*a(n-12) for n>20

%F k=4: a(n) = 442*a(n-3) +43*a(n-6) for n>15

%F k=5: a(n) = 442*a(n-3) +43*a(n-6) for n>16

%F k=6: a(n) = 442*a(n-3) +43*a(n-6) for n>17

%F k=7: a(n) = 442*a(n-3) +43*a(n-6) for n>18

%e Some solutions for n=3 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 17 2012