%I #6 Apr 11 2022 12:10:12

%S 297,1647,1647,9126,12987,9126,50571,102060,102060,50571,280233,

%T 802899,1134864,802899,280233,1552878,6320511,12647772,12647772,

%U 6320511,1552878,8605089,49756086,141199416,199953846,141199416,49756086,8605089

%N T(n,k) = Number of (n+2) X (k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.

%C Table starts

%C .....297......1647........9126........50571.........280233..........1552878

%C ....1647.....12987......102060.......802899........6320511.........49756086

%C ....9126....102060.....1134864.....12647772......141199416.......1576282464

%C ...50571....802899....12647772....199953846.....3170197872......50259172356

%C ..280233...6320511...141199416...3170197872....71502727077....1612681662123

%C .1552878..49756086..1576282464..50259172356..1612681662123...51750105608403

%C .8605089.391717269.17600380920.797070583521.36393871038174.1662024911503707

%H R. H. Hardin, <a href="/A253035/b253035.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-1) +3*a(n-2),

%F k=2: a(n) = 9*a(n-1) -5*a(n-2) -10*a(n-3) -174*a(n-4) +80*a(n-5) +160*a(n-6),

%F k=3: [order 20],

%F k=4: [order 72].

%e Some solutions for n=2, k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 26 2014