A298963 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 7, 3, 5, 0, 0, 8, 5, 14, 14, 5, 8, 0, 0, 13, 8, 34, 31, 34, 8, 13, 0, 0, 21, 13, 75, 91, 91, 75, 13, 21, 0, 0, 34, 21, 174, 230, 360, 230, 174, 21, 34, 0, 0, 55, 34, 396, 633, 1144, 1144, 633, 396, 34, 55, 0, 0, 89, 55

Offset

1,12

Comments

Table starts

.0..0..0...0....0.....0.....0......0.......0........0.........0.........0

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

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

.0..2..2...7...14....34....75....174.....396......907......2070......4734

.0..3..3..14...31....91...230....633....1685.....4552.....12185.....32765

.0..5..5..34...91...360..1144...4062...13794....47972....164529....567553

.0..8..8..75..230..1144..4263..18517...75262...317141...1307739...5446889

.0.13.13.174..633..4062.18517.101720..514070..2720154..14017132..73173545

.0.21.21.396.1685.13794.75262.514070.3172536.20741504.130945779.840773447

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

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

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

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

k=5: [order 11]

k=6: [order 30]

Example

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

Crossrefs

Columns 2 and 3 are A000045(n-1).

Sequence in context: A298167 A298957 A298902 * A180760 A233270 A241291

Adjacent sequences: A298960 A298961 A298962 * A298964 A298965 A298966

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 30 2018

Status

approved