A298100 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 3, 1, 1, 3, 0, 0, 5, 0, 3, 0, 5, 0, 0, 8, 3, 7, 7, 3, 8, 0, 0, 13, 0, 20, 5, 20, 0, 13, 0, 0, 21, 7, 42, 70, 70, 42, 7, 21, 0, 0, 34, 2, 121, 134, 847, 134, 121, 2, 34, 0, 0, 55, 19, 291, 941, 2934, 2934, 941, 291, 19, 55, 0, 0, 89, 10, 782, 3028

Offset

1,12

Comments

Table starts

.0..0.0...0....0......0.......0........0..........0...........0.............0

.0..1.1...2....3......5.......8.......13.........21..........34............55

.0..1.0...1....0......3.......0........7..........2..........19............10

.0..2.1...3....7.....20......42......121........291.........782..........1987

.0..3.0...7....5.....70.....134......941.......3028.......15282.........61027

.0..5.3..20...70....847....2934....27671.....139992.....1031816.......5985115

.0..8.0..42..134...2934...16212...273251....2168179....29643572.....283552252

.0.13.7.121..941..27671..273251..6915147...95118943..1940454441...30542054392

.0.21.2.291.3028.139992.2168179.95118943.2015018055.72368534390.1813924173233

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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) +2*a(n-2) -a(n-3) +a(n-4) -2*a(n-5)

k=4: [order 16]

k=5: [order 61]

Example

Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..1..1..1
..0..0..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1
..0..0..0..1. .0..0..1..1. .1..0..0..0. .1..1..0..0. .0..0..0..0
..0..0..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0
..0..0..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0

Crossrefs

Column 2 is A000045(n-1).

Sequence in context: A193511 A254218 A263147 * A303636 A073274 A192323

Adjacent sequences: A298097 A298098 A298099 * A298101 A298102 A298103

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 12 2018

Status

approved