A299194 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 3, 13, 8, 13, 34, 9, 9, 34, 13, 21, 73, 19, 80, 19, 73, 21, 34, 203, 59, 220, 220, 59, 203, 34, 55, 594, 129, 518, 1539, 518, 129, 594, 55, 89, 1443, 355, 2466, 3704, 3704, 2466, 355, 1443, 89, 144, 4013, 891, 8609, 25097, 11459, 25097

Offset

1,2

Comments

Table starts

..1....2...3.....5......8......13.......21........34.........55...........89

..2....4...3....13.....34......73......203.......594.......1443.........4013

..3....3...3.....9.....19......59......129.......355........891.........2317

..5...13...9....80....220.....518.....2466......8609......26954.......108253

..8...34..19...220...1539....3704....25097....161188.....638942......3784977

.13...73..59...518...3704...11459....80188....533274....2432710.....15899938

.21..203.129..2466..25097...80188...848789...8080772...44495267....401953734

.34..594.355..8609.161188..533274..8080772.122310309..832353461..10703053961

.55.1443.891.26954.638942.2432710.44495267.832353461.6602925250.104043829095

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..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..0
..0..0..0..0. .0..1..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..1
..1..1..1..1. .1..1..1..0. .0..0..1..0. .0..0..0..0. .1..1..1..1
..0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..0
..1..1..1..0. .0..1..1..0. .1..1..1..0. .1..0..0..1. .0..0..0..1

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A297901.

Sequence in context: A298501 A298320 A299393 * A300030 A232451 A299451

Adjacent sequences: A299191 A299192 A299193 * A299195 A299196 A299197

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 04 2018

Status

approved