A299602 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 9, 6, 0, 0, 17, 27, 27, 17, 0, 0, 41, 147, 130, 147, 41, 0, 0, 104, 643, 1241, 1241, 643, 104, 0, 0, 261, 3051, 8825, 21367, 8825, 3051, 261, 0, 0, 655, 14539, 72751, 290941, 290941, 72751, 14539, 655, 0, 0, 1646, 69087, 589816, 4309263

Offset

1,8

Comments

Table starts

.0...0.....0.......0.........0............0..............0................0

.0...1.....3.......6........17...........41............104..............261

.0...3.....9......27.......147..........643...........3051............14539

.0...6....27.....130......1241.........8825..........72751...........589816

.0..17...147....1241.....21367.......290941........4309263.........63960652

.0..41...643....8825....290941......7242300......197267780.......5361395737

.0.104..3051...72751...4309263....197267780.....9743385598.....481541186894

.0.261.14539..589816..63960652...5361395737...481541186894...43313516068423

.0.655.69087.4803248.948323066.145483752329.23753464370841.3889298014550366

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 13] for n>15

k=4: [order 48]

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .1..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
..0..1..1..1. .1..1..0..0. .0..0..1..1. .0..0..0..0. .1..0..0..1
..0..0..1..1. .1..1..1..0. .0..0..0..1. .0..0..0..0. .1..1..1..1

Crossrefs

Column 2 is A297972.

Sequence in context: A299334 A268759 A298841 * A299554 A300175 A129533

Adjacent sequences: A299599 A299600 A299601 * A299603 A299604 A299605

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 14 2018

Status

approved