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

Author

R. H. Hardin, Apr 24 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Row 2 is A302266.

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