A232295 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally

1, 3, 1, 7, 15, 1, 15, 97, 73, 1, 33, 587, 1313, 355, 1, 73, 3615, 20563, 17759, 1727, 1, 161, 22387, 336079, 718483, 240241, 8401, 1, 355, 138505, 5546705, 31119789, 25116353, 3249889, 40867, 1, 783, 856719, 91293443, 1370434057, 2885285507

Offset

1,2

Comments

Table starts

.1......3..........7.............15.................33.....................73

.1.....15.........97............587...............3615..................22387

.1.....73.......1313..........20563.............336079................5546705

.1....355......17759.........718483...........31119789.............1370434057

.1...1727.....240241.......25116353.........2885285507...........339565321435

.1...8401....3249889......877968487.......267483142619.........84130295708483

.1..40867...43963319....30690409685.....24797475083765......20843967523877175

.1.198799..594719777..1072818688305...2298890419506403....5164265865545602229

.1.967065.8045152705.37501616113029.213122398219612007.1279489656786836660869

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 4*a(n-1) +4*a(n-2) +a(n-3)

k=3: a(n) = 12*a(n-1) +20*a(n-2) +9*a(n-3)

k=4: [order 10]

k=5: [order 13] for n>14

k=6: [order 37] for n>38

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-3)

n=2: [order 9]

n=3: [order 31]

Example

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

Crossrefs

Row 1 is A193641

Sequence in context: A219063 A218810 A218638 * A228763 A101845 A193606

Adjacent sequences: A232292 A232293 A232294 * A232296 A232297 A232298

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2013

Status

approved