A274749 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.

1, 1, 1, 2, 3, 2, 4, 8, 9, 4, 8, 22, 34, 27, 8, 16, 60, 133, 144, 81, 16, 32, 164, 518, 813, 610, 243, 32, 64, 448, 2017, 4554, 4967, 2584, 729, 64, 128, 1224, 7858, 25585, 40242, 30349, 10946, 2187, 128, 256, 3344, 30605, 143634, 327123, 355504, 185435, 46368

Offset

1,4

Comments

Table starts

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

...1.....3......8.......22.........60..........164...........448

...2.....9.....34......133........518.........2017..........7858

...4....27....144......813.......4554........25585........143634

...8....81....610.....4967......40242.......327123.......2661918

..16...243...2584....30349.....355504......4190533......49475642

..32...729..10946...185435....3140840.....53680592.....920432562

..64..2187..46368..1133025...27748676....687685512...17123659885

.128..6561.196418..6922887..245154340...8809672678..318581114142

.256.19683.832040.42299477.2165891856.112857546696.5927090659144

Links

R. H. Hardin, Table of n, a(n) for n = 1..363

Formula

Empirical for column k:

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

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

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

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

k=5: a(n) = 9*a(n-1) -14*a(n-3) +10*a(n-4) -2*a(n-5) for n>6

k=6: [order 9] for n>11

k=7: [order 13] for n>15

Empirical for row n:

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

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

n=3: a(n) = 2*a(n-1) +7*a(n-2) +2*a(n-3) -2*a(n-4)

n=4: [order 8]

n=5: [order 16] for n>17

n=6: [order 36] for n>38

n=7: [order 80] for n>83

Example

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

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A000244(n-1).

Column 3 is A014445.

Row 1 is A000079(n-2).

Row 2 is A028859(n-1).

Sequence in context: A154578 A059576 A274803 * A247936 A231150 A274858

Adjacent sequences: A274746 A274747 A274748 * A274750 A274751 A274752

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 04 2016

Status

approved