A302265 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 153, 128, 16, 32, 384, 772, 818, 512, 32, 64, 1405, 3818, 5922, 4386, 2048, 64, 128, 5135, 19191, 40296, 45717, 23516, 8192, 128, 256, 18766, 96004, 284428, 429854, 353229, 126162, 32768, 256, 512, 68589, 481261

Offset

1,2

Comments

Table starts

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

...2......8......29.......105........384.........1405..........5135

...4.....32.....153.......772.......3818........19191.........96004

...8....128.....818......5922......40296.......284428.......1984001

..16....512....4386.....45717.....429854......4289139......41994750

..32...2048...23516....353229....4608075.....64975832.....893462062

..64...8192..126162...2727755...49315068....982041385...18964765818

.128..32768..676988..21069318..527911860..14850510984..402597400706

.256.131072.3632880.162753849.5651844495.224584502616.8547940665506

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: a(n) = 6*a(n-1) -2*a(n-2) +2*a(n-3) -54*a(n-4) +16*a(n-5) for n>6

k=4: [order 17] for n>18

k=5: [order 70] for n>71

Empirical for row n:

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

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

n=3: [order 12] for n>13

n=4: [order 44] for n>45

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..1..0
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..0. .1..0..1..1
..1..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..1. .1..1..0..0
..0..1..1..1. .1..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..1
..1..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..1..0. .1..1..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Sequence in context: A326105 A300811 A301450 * A302965 A302808 A303469

Adjacent sequences: A302262 A302263 A302264 * A302266 A302267 A302268

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2018

Status

approved