A316801 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 5, 6, 7 or 8 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, 18897, 32193, 18897, 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.....18897......91138......476043

.0..33...92...581...3759....32193....213931....1526824....11680344

.0..72..264..2184..18897...213931...1964108...19450547...202140736

.0.133..784..7680..91138..1526824..19450547..268526785..3980862756

.0.278.2378.28315.476043.11680344.202140736.3980862756.85266493095

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..0..0..0. .0..0..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..1..1..1..1. .1..1..0..1. .1..0..1..1. .1..1..0..1. .1..0..1..1
..1..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..1..0..1. .0..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..0..0
..0..1..1..0. .1..0..0..0. .1..0..0..1. .0..1..1..0. .0..1..1..1

Crossrefs

Column 2 is A304257.

Column 3 is A305218.

Column 4 is A305219.

Sequence in context: A240455 A304263 A305223 * A143044 A350789 A361357

Adjacent sequences: A316798 A316799 A316800 * A316802 A316803 A316804

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 14 2018

Status

approved