A298660 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 177, 173, 63, 177, 21, 34, 359, 96, 322, 431, 431, 322, 96, 359, 34, 55, 705, 147, 635, 876, 1116, 876, 635, 147, 705, 55, 89, 1351

Offset

1,5

Comments

Table starts

..0...1...1....2....3.....5.....8.....13......21......34.......55........89

..1...3...7...13...23....49....95....177.....359.....705.....1351......2689

..1...7..15...19...23....34....63.....96.....147.....233......368.......588

..2..13..19...40...85...173...322....635....1325....2806.....5877.....12293

..3..23..23...85..177...431...876...2137....5002...11687....27591.....64253

..5..49..34..173..431..1116..2562...6711...17405...48462...125671....334571

..8..95..63..322..876..2562..7964..24801...74358..242072...745571...2349275

.13.177..96..635.2137..6711.24801..89543..322065.1213296..4468276..16453935

.21.359.147.1325.5002.17405.74358.322065.1367704.6098314.26543249.116098205

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6

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

k=4: [order 72] for n>73

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A298050.

Sequence in context: A298093 A298055 A298888 * A299612 A297959 A298775

Adjacent sequences: A298657 A298658 A298659 * A298661 A298662 A298663

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2018

Status

approved