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

Author

R. H. Hardin, Jul 04 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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).

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