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

Author

R. H. Hardin, Jul 30 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A003945(n-2).

Row 1 is A007051(n-1).

Row 3 is A055842.

Row 4 is A108051(n+1).

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