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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. 7
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 (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.....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

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Last modified October 1 19:48 EDT 2022. Contains 357172 sequences. (Running on oeis4.)