A275504 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,-1) and new values introduced in order 0..2.

1, 2, 2, 5, 9, 3, 14, 54, 16, 6, 41, 324, 80, 28, 12, 122, 1944, 400, 136, 56, 24, 365, 11664, 2000, 656, 232, 104, 48, 1094, 69984, 10000, 3168, 988, 516, 200, 96, 3281, 419904, 50000, 15296, 4180, 2628, 1168, 380, 192, 9842, 2519424, 250000, 73856, 17712

Offset

1,2

Comments

Table starts

...1....2.....5.....14......41......122.......365.......1094........3281

...2....9....54....324....1944....11664.....69984.....419904.....2519424

...3...16....80....400....2000....10000.....50000.....250000.....1250000

...6...28...136....656....3168....15296.....73856.....356608.....1721856

..12...56...232....988....4180....17712.....75024.....317812.....1346268

..24..104...516...2628...13384....68080....346528....1763408.....8974288

..48..200..1168...7140...43780...268152...1643372...10069540....61703488

..96..380..2660..19368..143784..1063756...7886280...58423188...432942008

.192..724..6024..52864..470352..4220952..37846556..339516412..3045734096

.384.1380.13716.144228.1549756.16808164.182923008.1989999904.21655912500

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) for n>3

k=2: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>6

k=3: a(n) = 2*a(n-1) +2*a(n-2) -2*a(n-3) -4*a(n-4) +3*a(n-5) +a(n-6) -a(n-7) for n>11

k=4: [order 16] for n>20

k=5: [order 32] for n>36

k=6: [order 64] for n>68

Empirical for row n:

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

n=2: a(n) = 6*a(n-1) for n>2

n=3: a(n) = 5*a(n-1) for n>2

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

n=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3)

n=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>5

n=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>6

Example

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

Crossrefs

Column 1 is A003945(n-2).

Row 1 is A007051(n-1).

Row 3 is A055842.

Row 4 is A108051(n+1).

Sequence in context: A076949 A040009 A227527 * A275401 A011273 A274068

Adjacent sequences: A275501 A275502 A275503 * A275505 A275506 A275507

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 30 2016

Status

approved