A301400 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 3, 4, 0, 0, 9, 13, 13, 9, 0, 0, 19, 44, 78, 44, 19, 0, 0, 41, 156, 446, 446, 156, 41, 0, 0, 88, 554, 2619, 4857, 2619, 554, 88, 0, 0, 189, 1963, 15538, 49325, 49325, 15538, 1963, 189, 0, 0, 406, 6964, 92338, 521514, 885003, 521514

Offset: 1

Author

R. H. Hardin, Mar 20 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....3.....13.......44........156..........554...........1963

.0...4...13.....78......446.......2619........15538..........92338

.0...9...44....446.....4857......49325.......521514........5457161

.0..19..156...2619....49325.....885003.....16325745......299552320

.0..41..554..15538...521514...16325745....528025038....16971131642

.0..88.1963..92338..5457161..299552320..16971131642...956047339302

.0.189.6964.549096.57311190.5507220522.546618326745.53967719265287

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..263

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 45]