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A282275 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards. 5
1, 2, 2, 5, 14, 5, 14, 121, 121, 14, 41, 1085, 2992, 1085, 41, 122, 9729, 75413, 75413, 9729, 122, 365, 87238, 1899634, 5432319, 1899634, 87238, 365, 1094, 782246, 47863268, 390546284, 390546284, 47863268, 782246, 1094, 3281, 7014246 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2.....14........121..........1085.............9729...............87238

...5....121.......2992.........75413..........1899634............47863268

..14...1085......75413.......5432319........390546284.........28094166670

..41...9729....1899634.....390546284......80034513705......16416580121620

.122..87238...47863268...28094166670...16416580121620....9604952929717842

.365.782246.1205981686.2020997096826.3367389843804209.5619690409304729594

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..84

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) +8*a(n-2) +6*a(n-3) for n>5

k=3: [order 10] for n>11

k=4: [order 29] for n>30

EXAMPLE

Some solutions for n=3 k=4

..0..1..0..1. .0..0..0..1. .0..1..2..0. .0..1..1..2. .0..1..0..0

..2..2..0..1. .2..2..1..1. .2..1..2..2. .0..1..2..0. .0..0..0..1

..1..2..1..2. .0..1..1..0. .0..1..2..0. .1..2..1..0. .2..1..2..1

CROSSREFS

Column 1 is A007051(n-1).

Column 2 is A206628(n-1).

Sequence in context: A199655 A241114 A208392 * A208201 A185966 A032097

Adjacent sequences:  A282272 A282273 A282274 * A282276 A282277 A282278

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 10 2017

STATUS

approved

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Last modified March 25 12:50 EDT 2019. Contains 321470 sequences. (Running on oeis4.)