A305223 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 5, 6 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, 15, 15, 18, 0, 0, 33, 31, 49, 31, 33, 0, 0, 72, 92, 170, 170, 92, 72, 0, 0, 133, 264, 581, 792, 581, 264, 133, 0, 0, 278, 784, 2184, 3759, 3759, 2184, 784, 278, 0, 0, 541, 2378, 7680, 18876, 32193, 18876, 7680, 2378, 541, 0, 0

Offset

1,5

Comments

Table starts

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

.0...3....4.....9.....18.......33........72........133.........278

.0...4....8....15.....31.......92.......264........784........2378

.0...9...15....49....170......581......2184.......7680.......28315

.0..18...31...170....792.....3759.....18876......90956......474685

.0..33...92...581...3759....32193....212231....1501520....11428272

.0..72..264..2184..18876...212231...1893682...18341237...187726549

.0.133..784..7680..90956..1501520..18341237..246793217..3592452354

.0.278.2378.28315.474685.11428272.187726549.3592452354.75341044066

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 15] for n>18

k=4: [order 65] for n>66

Example

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

Crossrefs

Column 2 is A304257.

Sequence in context: A259191 A240455 A304263 * A316801 A143044 A350789

Adjacent sequences: A305220 A305221 A305222 * A305224 A305225 A305226

Keyword

nonn,tabl

Author

R. H. Hardin, May 27 2018

Status

approved