A299366 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 23, 42, 1, 1, 127, 125, 125, 127, 1, 1, 389, 420, 1157, 420, 389, 1, 1, 1192, 1943, 8134, 8134, 1943, 1192, 1, 1, 3645, 9012, 66668, 107653, 66668, 9012, 3645, 1, 1, 11161, 42321, 564283, 1640199, 1640199, 564283, 42321

Offset

1,5

Comments

Table starts

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

.1.....5.....13.......42........127...........389............1192

.1....13.....23......125........420..........1943............9012

.1....42....125.....1157.......8134.........66668..........564283

.1...127....420.....8134.....107653.......1640199........25838859

.1...389...1943....66668....1640199......45416563......1301827631

.1..1192...9012...564283...25838859....1301827631.....67756659422

.1..3645..42321..4792366..404080073...37042505019...3508332244817

.1.11161.205597.41273307.6401182687.1066728270636.183583736926115

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)

k=3: [order 12] for n>14

k=4: [order 46] for n>48

Example

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

Crossrefs

Column 2 is A298234.

Sequence in context: A272644 A157177 A298240 * A299135 A299893 A299060

Adjacent sequences: A299363 A299364 A299365 * A299367 A299368 A299369

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 08 2018

Status

approved