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A305015 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 14, 10, 3, 5, 51, 31, 31, 51, 5, 8, 165, 99, 42, 99, 165, 8, 13, 306, 206, 255, 255, 206, 306, 13, 21, 993, 455, 862, 2715, 862, 455, 993, 21, 34, 2867, 1321, 2200, 9499, 9499, 2200, 1321, 2867, 34, 55, 6818, 3108, 8807, 30457 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0....1....1.....2.......3.......5........8........13.........21..........34

..1....3...11....10......51.....165......306.......993.......2867........6818

..1...11...14....31......99.....206......455......1321.......3108........7353

..2...10...31....42.....255.....862.....2200......8807......33055......106158

..3...51...99...255....2715....9499....30457....225009....1046863.....4428355

..5..165..206...862....9499...28477...119835....975646....4538929....21859448

..8..306..455..2200...30457..119835...640900...6449924...41160483...271320922

.13..993.1321..8807..225009..975646..6449924.108290760..866160130..7324403720

.21.2867.3108.33055.1046863.4538929.41160483.866160130.7783586346.84091029541

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) +a(n-2)

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

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

k=4: [order 69] for n>70

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A305452 A304704 A316455 * A316648 A316176 A317458

Adjacent sequences:  A305012 A305013 A305014 * A305016 A305017 A305018

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 23 2018

STATUS

approved

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Last modified July 25 18:20 EDT 2021. Contains 346291 sequences. (Running on oeis4.)