A304263 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 4, 4, 0, 0, 9, 8, 9, 0, 0, 18, 13, 13, 18, 0, 0, 33, 17, 19, 17, 33, 0, 0, 72, 26, 47, 47, 26, 72, 0, 0, 133, 61, 88, 116, 88, 61, 133, 0, 0, 278, 120, 181, 230, 230, 181, 120, 278, 0, 0, 541, 233, 376, 772, 925, 772, 376, 233, 541, 0, 0, 1084, 515, 878, 1832

Offset

1,5

Comments

Table starts

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

.0...3...4...9...18....33.....72....133.....278......541......1084......2169

.0...4...8..13...17....26.....61....120.....233......515.......959......2203

.0...9..13..19...47....88....181....376.....878.....2001......4424.....10341

.0..18..17..47..116...230....772...1832....5500....15852.....43779....127396

.0..33..26..88..230...925...2516...8248...27317....89074....287896....945232

.0..72..61.181..772..2516..10024..35769..143364...546403...2127606...8299219

.0.133.120.376.1832..8248..35769.185874..883660..4100466..20201440..96805441

.0.278.233.878.5500.27317.143364.883660.4991758.27273238.158873103.901602511

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

k=3: [order 17] for n>18

k=4: [order 63] for n>64

Example

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

Crossrefs

Sequence in context: A288654 A259191 A240455 * A305223 A316801 A143044

Adjacent sequences: A304260 A304261 A304262 * A304264 A304265 A304266

Keyword

nonn,tabl

Author

R. H. Hardin, May 09 2018

Status

approved