A298930 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 3, 11, 3, 13, 0, 0, 34, 7, 23, 23, 7, 34, 0, 0, 65, 14, 72, 94, 72, 14, 65, 0, 0, 123, 35, 201, 255, 255, 201, 35, 123, 0, 0, 266, 89, 597, 666, 955, 666, 597, 89, 266, 0, 0, 499, 242, 1717, 2720, 3569, 3569, 2720

Offset

1,8

Comments

Table starts

.0...0..0....0....0.....0......0.......0........0.........0.........0

.0...1..3....2...11....13.....34......65......123.......266.......499

.0...3..1....4....3.....7.....14......35.......89.......242.......643

.0...2..4...11...23....72....201.....597.....1717......5183.....15479

.0..11..3...23...94...255....666....2720.....8571.....30093....106192

.0..13..7...72..255...955...3569...15031....61046....253624...1067751

.0..34.14..201..666..3569..15163...77576...375845...1886321...9434661

.0..65.35..597.2720.15031..77576..491338..2806944..16889645.100996053

.0.123.89.1717.8571.61046.375845.2806944.19329083.138482223.988954778

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 18] for n>19

k=4: [order 60] for n>61

Example

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

Crossrefs

Column 2 is A297870.

Column 3 is A298254.

Sequence in context: A298139 A298087 A298259 * A298895 A179311 A309983

Adjacent sequences: A298927 A298928 A298929 * A298931 A298932 A298933

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 29 2018

Status

approved