A303469 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 170, 128, 16, 32, 384, 948, 1033, 512, 32, 64, 1405, 5237, 9110, 6369, 2048, 64, 128, 5135, 29009, 79377, 89371, 39098, 8192, 128, 256, 18766, 160590, 692636, 1243692, 872026, 240109, 32768, 256, 512, 68589, 888993

Offset

1,2

Comments

Table starts

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

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

...4.....32.....170.......948........5237.........29009..........160590

...8....128....1033......9110.......79377........692636.........6051850

..16....512....6369.....89371.....1243692......17247543.......239939422

..32...2048...39098....872026....19374638.....427097893......9459086839

..64...8192..240109...8511918...302023677...10589284528....373571747330

.128..32768.1476141..83188773..4716032889..263136262937..14793218857797

.256.131072.9071642.812770434.73624207904.6538180319944.585806882371397

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) = 7*a(n-1) -5*a(n-2) +20*a(n-3) -144*a(n-4) +72*a(n-5) for n>6

k=4: [order 20] for n>21

k=5: [order 93] for n>94

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 14] for n>15

n=4: [order 49] for n>50

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Row 2 is A302266.

Sequence in context: A302265 A302965 A302808 * A281955 A316183 A305769

Adjacent sequences: A303466 A303467 A303468 * A303470 A303471 A303472

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 24 2018

Status

approved