A275037 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

1, 1, 2, 2, 6, 3, 4, 16, 18, 6, 8, 48, 46, 54, 12, 16, 144, 137, 146, 162, 24, 32, 432, 401, 570, 450, 486, 48, 64, 1296, 1152, 2185, 2334, 1428, 1458, 96, 128, 3888, 3336, 8273, 11624, 9774, 4463, 4374, 192, 256, 11664, 9720, 31495, 57984, 64045, 40572, 14086

Offset: 1

Author

R. H. Hardin, Jul 14 2016

Keywords

• nonn
• tabl

Comments

Table starts

...1.....1......2.......4........8.........16..........32...........64

...2.....6.....16......48......144........432........1296.........3888

...3....18.....46.....137......401.......1152........3336.........9720

...6....54....146.....570.....2185.......8273.......31495.......120845

..12...162....450....2334....11624......57984......290927......1465435

..24...486...1428....9774....64045.....421793.....2788663.....18527905

..48..1458...4463...40572...351197....3056856....26631796....233894638

..96..4374..14086..169348..1931619...22207559...255796423...2976710318

.192.13122..44195..704704.10581148..160767947..2451632155..37779884891

.384.39366.139130.2937764.58059378.1166126087.23548292980.480461388679

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..338

Crossrefs

Column 1 is A003945(n-2).

Column 2 is A008776(n-1).

Row 1 is A000079(n-2).

Formula

Empirical for column k:

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

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

k=3: [order 16] for n>17

k=4: [order 35] for n>37

k=5: [order 70] for n>74

Empirical for row n:

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

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

n=3: [order 9] for n>10

n=4: [order 17] for n>19

n=5: [order 28] for n>32

n=6: [order 67] for n>72