A301541 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 6, 6, 5, 8, 10, 9, 10, 8, 13, 21, 26, 26, 21, 13, 21, 42, 61, 79, 61, 42, 21, 34, 86, 154, 212, 212, 154, 86, 34, 55, 179, 374, 603, 658, 603, 374, 179, 55, 89, 370, 941, 1841, 2417, 2417, 1841, 941, 370, 89, 144, 770, 2357, 5663, 9037, 10783, 9037

Offset

1,2

Comments

Table starts

..1...2....3.....5......8.....13......21.......34........55.........89

..2...3....6....10.....21.....42......86......179.......370........770

..3...6....9....26.....61....154.....374......941......2357.......5963

..5..10...26....79....212....603....1841.....5663.....17379......53565

..8..21...61...212....658...2417....9037....33526....125626.....477972

.13..42..154...603...2417..10783...47791...215362....990403....4616134

.21..86..374..1841...9037..47791..255406..1432328...8145489...46701775

.34.179..941..5663..33526.215362.1432328..9891331..68863154..484837793

.55.370.2357.17379.125626.990403.8145489.68863154.588765472.5132456266

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

k=3: [order 20]

k=4: [order 62]

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A240513.

Sequence in context: A260684 A029093 A369788 * A240519 A318037 A326165

Adjacent sequences: A301538 A301539 A301540 * A301542 A301543 A301544

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 23 2018

Status

approved