A252952 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

198, 747, 747, 2970, 2988, 2970, 11943, 12915, 12915, 11943, 48024, 57978, 64242, 57978, 48024, 193059, 262494, 334197, 334197, 262494, 193059, 776160, 1192149, 1784781, 2101338, 1784781, 1192149, 776160, 3120579, 5419521, 9627372, 13646115

Offset

1,1

Comments

Table starts

......198.......747.......2970........11943.........48024..........193059

......747......2988......12915........57978........262494.........1192149

.....2970.....12915......64242.......334197.......1784781.........9627372

....11943.....57978.....334197......2101338......13646115........90331596

....48024....262494....1784781.....13646115.....110574774.......919418760

...193059...1192149....9627372.....90331596.....919418760......9729661266

...776160...5419521...52118784....603797472....7763464440....104852356227

..3120579..24648309..282725568...4053062745...66003601788...1141808774769

.12546540.112122162.1535104449..27261133281..563165929260..12498557877783

.50444415.510068277.8338827870.183573601551.4814005980501.137122697754648

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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)

k=2: [order 22]

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

Example

Some solutions for n=3 k=4
..0..0..1..1..2..1....0..0..1..1..0..0....0..0..1..0..0..1....0..0..1..0..1..0
..0..2..2..1..2..2....2..1..1..2..1..2....1..0..1..1..2..1....2..0..2..2..0..0
..1..2..2..0..0..1....0..1..0..1..1..2....0..2..2..0..2..0....2..1..1..2..1..1
..1..0..0..1..0..1....2..2..1..1..2..1....1..0..1..0..1..1....1..0..1..1..0..1
..0..2..0..0..2..2....0..1..0..0..1..1....1..0..1..1..2..1....2..0..0..2..0..2

Crossrefs

Sequence in context: A066218 A304614 A357076 * A252945 A158222 A156771

Adjacent sequences: A252949 A252950 A252951 * A252953 A252954 A252955

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2014

Status

approved