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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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 A305151 A127775

Adjacent sequences:  A316798 A316799 A316800 * A316802 A316803 A316804

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 14 2018

STATUS

approved

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Last modified May 17 18:29 EDT 2021. Contains 343987 sequences. (Running on oeis4.)