A295781 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

2, 3, 3, 5, 9, 5, 8, 19, 19, 8, 13, 49, 56, 49, 13, 21, 123, 198, 198, 123, 21, 34, 297, 665, 1059, 665, 297, 34, 55, 739, 2213, 5263, 5263, 2213, 739, 55, 89, 1825, 7479, 25529, 37897, 25529, 7479, 1825, 89, 144, 4491, 25105, 127731, 262707, 262707, 127731

Offset: 1

Author

R. H. Hardin, Nov 27 2017

Keywords

• nonn
• tabl

Comments

Table starts

..2....3.....5.......8.......13.........21..........34............55

..3....9....19......49......123........297.........739..........1825

..5...19....56.....198......665.......2213........7479.........25105

..8...49...198....1059.....5263......25529......127731........630988

.13..123...665....5263....37897.....262707.....1905471......13577504

.21..297..2213...25529...262707....2602065....27085621.....276224518

.34..739..7479..127731..1905471...27085621...409525082....6037613762

.55.1825.25105..630988.13577504..276224518..6037613762..128171125105

.89.4491.84326.3118368.96726819.2819029784.89072774496.2722986415966

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..311

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A102001(n+1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +2*a(n-2) +4*a(n-3)

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

k=4: [order 10]

k=5: [order 22]

k=6: [order 43]

k=7: [order 91]