A298259 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 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, 86, 72, 14, 65, 0, 0, 123, 35, 201, 238, 238, 201, 35, 123, 0, 0, 266, 89, 597, 604, 895, 604, 597, 89, 266, 0, 0, 499, 242, 1705, 2492, 3335, 3335, 2492

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.....1705......5141.....15305

.0..11..3...23...86...238....604....2492.....7722.....26880.....93816

.0..13..7...72..238...895...3335...13980....55889....230402....953813

.0..34.14..201..604..3335..13991...70095...331341...1644480...8037526

.0..65.35..597.2492.13980..70095..435534..2412035..14299708..83146969

.0.123.89.1705.7722.55889.331341.2412035.16014301.112395697.777907073

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 53] for n>54

Example

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

Crossrefs

Column 2 is A297870.

Sequence in context: A297876 A298139 A298087 * A298930 A298895 A179311

Adjacent sequences: A298256 A298257 A298258 * A298260 A298261 A298262

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2018

Status

approved