A304952 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 29, 26, 29, 49, 1, 1, 99, 58, 70, 70, 58, 99, 1, 1, 194, 120, 139, 189, 139, 120, 194, 1, 1, 387, 250, 287, 468, 468, 287, 250, 387, 1, 1, 773, 515, 625, 1436, 1916, 1436, 625, 515, 773, 1, 1, 1538

Offset

1,5

Comments

Table starts

.1...1...1....1.....1.....1......1.......1........1........1.........1

.1...4...7...13....26....49.....99.....194......387......773......1538

.1...7..13...21....29....58....120.....250......515.....1100......2302

.1..13..21...26....70...139....287.....625.....1484.....3197......7321

.1..26..29...70...189...468...1436....3753....11101....32272.....92418

.1..49..58..139...468..1916...5296...17450....62128...207139....693887

.1..99.120..287..1436..5296..18950...76117...313593..1223755...4910872

.1.194.250..625..3753.17450..76117..401301..2043622..9772099..49480464

.1.387.515.1484.11101.62128.313593.2043622.12197817.69375211.421959328

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) for n>5

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

k=4: [order 70] for n>71

Example

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

Crossrefs

Column 2 is A304004.

Sequence in context: A316733 A304010 A305360 * A316620 A304676 A316123

Adjacent sequences: A304949 A304950 A304951 * A304953 A304954 A304955

Keyword

nonn,tabl

Author

R. H. Hardin, May 22 2018

Status

approved