A298454 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 0, 16, 0, 1, 48, 11, 11, 48, 1, 0, 88, 26, 161, 26, 88, 0, 1, 240, 46, 478, 478, 46, 240, 1, 0, 704, 204, 2459, 5938, 2459, 204, 704, 0, 1, 1600, 696, 15248, 22133, 22133, 15248, 696, 1600, 1, 0, 4032, 1493, 78163, 206239, 255029

Offset

1,5

Comments

Table starts

.0....1....0......1........0.........1...........0.............1

.1....4....4.....16.......48........88.........240...........704

.0....4....0.....11.......26........46.........204...........696

.1...16...11....161......478......2459.......15248.........78163

.0...48...26....478.....5938.....22133......206239.......2539477

.1...88...46...2459....22133....255029.....4095727......62979342

.0..240..204..15248...206239...4095727...112275165....2871621220

.1..704..696..78163..2539477..62979342..2871621220..141892377970

.0.1600.1493.390424.16116493.804773211.62756244756.4903035588074

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 17] for n>18

k=4: [order 53] for n>56

Example

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

Crossrefs

Sequence in context: A298924 A217476 A298622 * A298834 A299588 A299528

Adjacent sequences: A298451 A298452 A298453 * A298455 A298456 A298457

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2018

Status

approved