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.

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

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