A316648 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 15, 10, 3, 5, 51, 33, 33, 51, 5, 8, 165, 117, 42, 117, 165, 8, 13, 306, 247, 277, 277, 247, 306, 13, 21, 993, 599, 954, 3988, 954, 599, 993, 21, 34, 2867, 1757, 2432, 13869, 13869, 2432, 1757, 2867, 34, 55, 6818, 4241, 10541, 54941

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...15....33.....117.....247.......599.......1757........4241

..2...10...33....42.....277.....954......2432......10541.......39013

..3...51..117...277....3988...13869.....54941.....427096.....1946889

..5..165..247...954...13869...43604....228056....1976020.....9093873

..8..306..599..2432...54941..228056...1396674...17049299...106043303

.13..993.1757.10541..427096.1976020..17049299..331807728..2594184863

.21.2867.4241.39013.1946889.9093873.106043303.2594184863.22368384180

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]

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A304704 A316455 A305015 * A316176 A317458 A301615

Adjacent sequences: A316645 A316646 A316647 * A316649 A316650 A316651

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 09 2018

Status

approved