A300465 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 2, 4, 0, 0, 9, 8, 8, 9, 0, 0, 19, 22, 28, 22, 19, 0, 0, 41, 68, 142, 142, 68, 41, 0, 0, 88, 212, 540, 1146, 540, 212, 88, 0, 0, 189, 652, 2585, 7456, 7456, 2585, 652, 189, 0, 0, 406, 2017, 11343, 55663, 78195, 55663, 11343, 2017, 406, 0, 0

Offset: 1

Author

R. H. Hardin, Mar 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

.0...1....2.....4.......9........19.........41...........88............189

.0...2....2.....8......22........68........212..........652...........2017

.0...4....8....28.....142.......540.......2585........11343..........51501

.0...9...22...142....1146......7456......55663.......400028........2906875

.0..19...68...540....7456.....78195.....935121.....10913850......127028268

.0..41..212..2585...55663....935121...17675111....330639367.....6123205255

.0..88..652.11343..400028..10913850..330639367...9829599051...293961266876

.0.189.2017.51501.2906875.127028268.6123205255.293961266876.14061129641181

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 2 is A078039(n-2).

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 52] for n>54