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

Author

R. H. Hardin, Mar 23 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A240513.

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]