A300646 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 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, 10, 10, 9, 0, 0, 19, 30, 64, 30, 19, 0, 0, 41, 104, 316, 316, 104, 41, 0, 0, 88, 340, 1789, 2998, 1789, 340, 88, 0, 0, 189, 1144, 9738, 28089, 28089, 9738, 1144, 189, 0, 0, 406, 3795, 54293, 268615, 456649, 268615, 54293, 3795

Offset: 1

Author

R. H. Hardin, Mar 10 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

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

.0...2....2.....10.......30........104..........340...........1144

.0...4...10.....64......316.......1789.........9738..........54293

.0...9...30....316.....2998......28089.......268615........2552014

.0..19..104...1789....28089.....456649......7455411......121708555

.0..41..340...9738...268615....7455411....209156119.....5850560104

.0..88.1144..54293..2552014..121708555...5850560104...280782187131

.0.189.3795.300456.24338903.1990954802.164070075524.13506744672543

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

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 49]