A316455 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 9, 10, 3, 5, 51, 23, 23, 51, 5, 8, 165, 58, 48, 58, 165, 8, 13, 306, 126, 229, 229, 126, 306, 13, 21, 993, 272, 850, 1591, 850, 272, 993, 21, 34, 2867, 672, 3223, 6590, 6590, 3223, 672, 2867, 34, 55, 6818, 1553, 10880, 29406, 53863

Offset

1,5

Comments

Table starts

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

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

..1...11....9....23......58......126.......272.........672.........1553

..2...10...23....48.....229......850......3223.......10880........45692

..3...51...58...229....1591.....6590.....29406......180787......1110885

..5..165..126...850....6590....53863....349456.....3164734.....29901503

..8..306..272..3223...29406...349456...4145337....44700278....711845805

.13..993..672.10880..180787..3164734..44700278...935229204..23033473439

.21.2867.1553.45692.1110885.29901503.711845805.23033473439.873192441329

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

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>20

k=4: [order 67] for n>69

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..1
..1..0..0..1. .1..0..1..0. .0..0..0..0. .0..1..0..1. .1..0..0..1
..1..0..0..1. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
..1..1..1..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..1

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A304058 A305452 A304704 * A305015 A316648 A316176

Adjacent sequences: A316452 A316453 A316454 * A316456 A316457 A316458

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 03 2018

Status

approved