A297889 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 41, 36, 41, 137, 64, 128, 301, 67, 84, 84, 67, 301, 128, 256, 705, 99, 134, 114, 134, 99, 705, 256, 512, 1461, 156, 223, 162, 162, 223, 156, 1461, 512, 1024, 3193, 255, 396, 248, 253, 248

Offset

1,2

Comments

Table starts

...1....2...4...8..16..32..64.128..256..512.1024..2048..4096..8192..16384

...2....7..13..29..69.137.301.705.1461.3193.7373.15729.34405.78569.170813

...4...13..20..26..41..67..99.156..255..406..654..1075..1765..2903...4816

...8...29..26..36..84.134.223.396..638.1173.2157..3812..6922.12304..21936

..16...69..41..84.114.162.248.368..520..786.1308..2126..3136..5052...7740

..32..137..67.134.162.253.264.437..656..942.1308..2254..3113..4698...7376

..64..301..99.223.248.264.433.579..650.1124.1469..2441..3648..5209...7873

.128..705.156.396.368.437.579.734..864.1154.1711..2267..3028..4060...5423

.256.1461.255.638.520.656.650.864.1037.1248.1647..2362..2966..3994...5228

Links

R. H. Hardin, Table of n, a(n) for n = 1..1104

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

k=3: [order 10] for n>11

k=4: [order 30] for n>34

k=5: [order 86] for n>91

Example

Some solutions for n=7 k=4
..0..1..1..0. .0..0..1..1. .0..1..0..0. .0..1..1..1. .0..1..0..0
..0..0..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..1..1
..1..1..0..0. .0..1..0..1. .0..0..0..1. .1..1..0..0. .1..0..0..0
..0..0..1..1. .1..1..0..0. .1..0..1..0. .1..1..0..0. .0..1..0..1
..1..0..0..0. .1..1..0..0. .1..0..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..1. .0..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
..0..0..1..0. .1..1..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..1

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A220308 A203975 A270246 * A298294 A299388 A298494

Adjacent sequences: A297886 A297887 A297888 * A297890 A297891 A297892

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2018

Status

approved