A282056 T(n,k) = Number of n X k 0..2 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 5, 14, 5, 14, 91, 91, 14, 41, 600, 388, 600, 41, 122, 4039, 2754, 2754, 4039, 122, 365, 27212, 15543, 31752, 15543, 27212, 365, 1094, 183195, 95045, 237031, 237031, 95045, 183195, 1094, 3281, 1233336, 565516, 2109626, 2091092, 2109626, 565516

Offset

1,2

Comments

Table starts

....1........2.........5..........14...........41..........122...........365

....2.......14........91.........600.........4039........27212........183195

....5.......91.......388........2754........15543........95045........565516

...14......600......2754.......31752.......237031......2109626......17495647

...41.....4039.....15543......237031......2091092.....22779237.....235194056

..122....27212.....95045.....2109626.....22779237....299676213....3900134833

..365...183195....565516....17495647....235194056...3900134833...64606412468

.1094..1233336...3403942...148941378...2461439740..50732580694.1061812396215

.3281..8303647..20376721..1259597639..25939234980.672441825967

.9842.55905604.122289647.10659570010.271794661137

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -11*a(n-2) +20*a(n-3) -24*a(n-4) +8*a(n-5).

k=3: [order 16] for n > 18.

k=4: [order 41] for n > 45.

Example

Some solutions for n=4, k=4
..0..1..2..1. .0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..0..1
..1..0..0..2. .0..0..0..0. .1..0..0..0. .1..1..1..1. .0..0..0..0
..1..0..0..0. .0..0..0..1. .0..1..0..0. .1..1..1..1. .1..0..0..0
..2..0..0..2. .1..1..1..1. .1..1..1..2. .1..1..1..2. .1..0..0..0

Crossrefs

Column 1 is A007051(n-1).

Sequence in context: A208434 A336110 A275352 * A199655 A241114 A208392

Adjacent sequences: A282053 A282054 A282055 * A282057 A282058 A282059

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2017

Status

approved