A303325 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 8, 1, 8, 1, 8, 4, 2, 16, 1, 32, 1, 8, 1, 32, 1, 32, 4, 2, 16, 2, 64, 1, 128, 1, 12, 4, 32, 1, 128, 1, 128, 4, 10, 64, 3, 64, 2, 256, 1, 512, 1, 46, 25, 62, 3, 128, 1, 512, 1, 512, 4, 50, 368, 56, 204, 10, 256, 2, 1024, 1, 2048, 1, 204, 201, 758, 136, 744, 9, 512, 1

Offset

1,3

Comments

Table starts

...1.1...1..1...1....1.....1.....1.......1........1.........1..........1

...2.2...8..8..32...32...128...128.....512......512......2048.......2048

...4.1...4..1...4....1.....4.....1.......4........1.........4..........1

...8.2...8..2..12...10....46....50.....204......290......1034.......1682

..16.1..16..4..64...25...368...201....2545.....1855.....21082......17922

..32.2..32..3..62...56...758...822...11950....15100....206189.....274746

..64.1..64..3.204..136..2956..3929...69328...130531...2005898....4227664

.128.2.128.10.744..531.15494.24759..629227..1489177..33766564...89782726

.256.1.256..9.900.1035.44101.97205.3531980.11297739.359263250.1265799068

Links

R. H. Hardin, Table of n, a(n) for n = 1..242

Formula

Empirical for column k:

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

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

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

k=4: [order 55] for n>57

k=5: [order 33] for n>35

Empirical for row n:

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

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

n=3: a(n) = a(n-2)

n=4: [order 18] for n>19

n=5: [order 34] for n>35

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 3 is A000079(n-1) for n>2.

Row 2 is A158302(n+1).

Row 3 is A010685(n+8).

Sequence in context: A157751 A177701 A119765 * A077901 A105619 A302212

Adjacent sequences: A303322 A303323 A303324 * A303326 A303327 A303328

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 21 2018

Status

approved