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

1,5

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A180762.

Sequence in context: A316648 A316176 A317458 * A180771 A300546 A300973

Adjacent sequences: A301612 A301613 A301614 * A301616 A301617 A301618

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 24 2018

Status

approved