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

1,3

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

Links

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

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

Example

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

Crossrefs

Column 1 is A003945(n-2).

Column 2 is A008776(n-1).

Row 1 is A000079(n-2).

Sequence in context: A182701 A277011 A277021 * A174833 A085738 A227608

Adjacent sequences: A275034 A275035 A275036 * A275038 A275039 A275040

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 14 2016

Status

approved