A276248 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-2) and new values introduced in order 0..2.

1, 2, 2, 3, 9, 5, 6, 24, 36, 14, 12, 72, 85, 144, 41, 24, 216, 279, 347, 576, 122, 48, 648, 900, 1447, 1404, 2304, 365, 96, 1944, 2837, 6372, 7316, 5671, 9216, 1094, 192, 5832, 9148, 26325, 43662, 36744, 23000, 36864, 3281, 384, 17496, 29570, 115682, 234431

Offset: 1

Author

R. H. Hardin, Aug 25 2016

Keywords

• nonn
• tabl

Comments

Table starts

....1......2.......3........6........12..........24...........48.............96

....2......9......24.......72.......216.........648.........1944...........5832

....5.....36......85......279.......900........2837.........9148..........29570

...14....144.....347.....1447......6372.......26325.......115682.........509750

...41....576....1404.....7316.....43662......234431......1423062........8496628

..122...2304....5671....36744....291113.....2069454.....17450554......141165944

..365...9216...23000...188696...2003694....18671229....219977330.....2410124377

.1094..36864...93204...966555..13727745...167951009...2780927371....41132001645

.3281.147456..377421..4951790..93489265..1509288801..35144231606...700435484735

.9842.589824.1529844.25428687.640009243.13609728840.446083313365.11973407175492

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A002063(n-2).

Row 1 is A003945(n-2).

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -4*a(n-2) +17*a(n-3) -83*a(n-4) +54*a(n-5) +56*a(n-6) for n>9

k=4: [order 36] for n>37

k=5: [order 41] for n>45

Empirical for row n:

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

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

n=3: [order 14] for n>15

n=4: [order 57] for n>60