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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)