A301662 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 6, 6, 6, 8, 13, 9, 9, 9, 9, 13, 21, 14, 15, 13, 15, 14, 21, 34, 22, 26, 24, 24, 26, 22, 34, 55, 35, 46, 45, 46, 45, 46, 35, 55, 89, 56, 83, 89, 99, 99, 89, 83, 56, 89, 144, 90, 151, 182, 223, 254, 223, 182, 151, 90, 144, 233, 145, 276, 373, 528, 696

Offset: 1

Author

R. H. Hardin, Mar 25 2018

Keywords

• nonn
• tabl

Comments

Table starts

..1..2...3...5....8...13....21.....34......55......89......144.......233

..2..3...4...6....9...14....22.....35......56......90......145.......234

..3..4...6...9...15...26....46.....83.....151.....276......506.......929

..5..6...9..13...24...45....89....182.....373.....773.....1604......3333

..8..9..15..24...46...99...223....528....1268....3085.....7557.....18564

.13.14..26..45...99..254...696...2013....5953...17878....54126....164525

.21.22..46..89..223..696..2335...8380...31001..116558...442314...1686894

.34.35..83.182..528.2013..8380..37679..175638..833737..4001569..19319239

.55.56.151.373.1268.5953.31001.175638.1036686.6245327.38085186.233683529

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..544

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A001611(n+1).

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-3)

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

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

k=5: [order 11]

k=6: [order 18]

k=7: [order 31]