A299221 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 37, 22, 37, 1, 1, 104, 81, 81, 104, 1, 1, 301, 307, 427, 307, 301, 1, 1, 864, 1201, 2338, 2338, 1201, 864, 1, 1, 2485, 5066, 13458, 21730, 13458, 5066, 2485, 1, 1, 7144, 21292, 84948, 202841, 202841, 84948, 21292, 7144, 1, 1, 20541

Offset

1,5

Comments

Table starts

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

.1....5....12......37.......104.........301..........864...........2485

.1...12....22......81.......307........1201.........5066..........21292

.1...37....81.....427......2338.......13458........84948.........543741

.1..104...307....2338.....21730......202841......1992466.......19685956

.1..301..1201...13458....202841.....3096833.....48911434......775504649

.1..864..5066...84948...1992466....48911434...1226106440....30729398000

.1.2485.21292..543741..19685956...775504649..30729398000..1213390065190

.1.7144.90443.3534493.195564094.12397088059.778116037031.48505143319432

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) = 5*a(n-2) +8*a(n-3) +4*a(n-4),

k=3: [order 19] for n>20,

k=4: [order 66] for n>68.

Example

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

Crossrefs

Column 2 is A297909.

Sequence in context: A297915 A298508 A298328 * A300035 A130227 A114123

Adjacent sequences: A299218 A299219 A299220 * A299222 A299223 A299224

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2018

Status

approved