A252952 - OEIS

%I #4 Dec 25 2014 07:06:31

%S 198,747,747,2970,2988,2970,11943,12915,12915,11943,48024,57978,64242,

%T 57978,48024,193059,262494,334197,334197,262494,193059,776160,1192149,

%U 1784781,2101338,1784781,1192149,776160,3120579,5419521,9627372,13646115

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

%C Table starts

%C ......198.......747.......2970........11943.........48024..........193059

%C ......747......2988......12915........57978........262494.........1192149

%C .....2970.....12915......64242.......334197.......1784781.........9627372

%C ....11943.....57978.....334197......2101338......13646115........90331596

%C ....48024....262494....1784781.....13646115.....110574774.......919418760

%C ...193059...1192149....9627372.....90331596.....919418760......9729661266

%C ...776160...5419521...52118784....603797472....7763464440....104852356227

%C ..3120579..24648309..282725568...4053062745...66003601788...1141808774769

%C .12546540.112122162.1535104449..27261133281..563165929260..12498557877783

%C .50444415.510068277.8338827870.183573601551.4814005980501.137122697754648

%H R. H. Hardin, <a href="/A252952/b252952.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3) +2*a(n-4) -6*a(n-5) +4*a(n-6)

%F k=2: [order 22]

%F k=3: [order 61] for n>63

%e Some solutions for n=3 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 25 2014