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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A102001(n+1).

Sequence in context: A059503 A317644 A194000 * A296725 A296588 A065460

Adjacent sequences: A295778 A295779 A295780 * A295782 A295783 A295784

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2017

Status

approved