A305015 - OEIS

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.

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