A301615 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 34, 62, 34, 3, 5, 111, 367, 367, 111, 5, 8, 361, 2131, 3816, 2131, 361, 8, 13, 1172, 12467, 40085, 40085, 12467, 1172, 13, 21, 3809, 72758, 421025, 758338, 421025, 72758, 3809, 21, 34, 12377, 425003, 4422826, 14345706, 14345706

Offset: 1

Author

R. H. Hardin, Mar 24 2018

Keywords

• nonn
• tabl

Comments

Table starts

..0.....1.......1.........2...........3..............5................8

..1.....3......11........34.........111............361.............1172

..1....11......62.......367........2131..........12467............72758

..2....34.....367......3816.......40085.........421025..........4422826

..3...111....2131.....40085......758338.......14345706........271301458

..5...361...12467....421025....14345706......488491106......16632517333

..8..1172...72758...4422826...271301458....16632517333....1019565752074

.13..3809..425003..46459647..5131197358...566336198475...62500458737127

.21.12377.2481842.488047397.97045266159.19283659583317.3831336753439723

Examples

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

Links

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A180762.

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)

k=3: [order 10]

k=4: [order 20] for n>21

k=5: [order 68] for n>69