A298782 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 6, 2, 1, 1, 5, 2, 2, 5, 1, 1, 9, 4, 4, 4, 9, 1, 1, 22, 7, 11, 11, 7, 22, 1, 1, 45, 8, 26, 37, 26, 8, 45, 1, 1, 101, 15, 76, 178, 178, 76, 15, 101, 1, 1, 218, 23, 222, 139, 562, 139, 222, 23, 218, 1, 1, 477, 38, 721, 823, 2607, 2607, 823, 721, 38, 477

Offset

1,12

Comments

Table starts

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

.1...1..1...2....5.....9.....22.......45.......101........218..........477

.1...1..6...2....4.....7......8.......15........23.........38...........61

.1...2..2...4...11....26.....76......222.......721.......2361.........7737

.1...5..4..11...37...178....139......823......3906......12610........55215

.1...9..7..26..178...562...2607....15018.....81636.....455586......2645277

.1..22..8..76..139..2607...9889....75446....868689....7675611.....76328995

.1..45.15.222..823.15018..75446..1477645..18375492..261985685...3562741942

.1.101.23.721.3906.81636.868689.18375492.403292040.8471002968.176635665084

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +a(n-2) for n>7

k=4: [order 21] for n>27

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A010590 A049061 A342670 * A082516 A318709 A204935

Adjacent sequences: A298779 A298780 A298781 * A298783 A298784 A298785

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2018

Status

approved