A298917 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 5, 3, 3, 3, 5, 1, 1, 8, 5, 4, 4, 5, 8, 1, 1, 13, 8, 6, 7, 6, 8, 13, 1, 1, 21, 13, 9, 9, 9, 9, 13, 21, 1, 1, 34, 21, 14, 15, 14, 15, 14, 21, 34, 1, 1, 55, 34, 22, 26, 24, 24, 26, 22, 34, 55, 1, 1, 89, 55, 35, 46, 44, 40, 44, 46, 35, 55

Offset: 1

Author

R. H. Hardin, Jan 29 2018

Keywords

• nonn
• tabl

Comments

Table starts

.1..1..1..1..1..1...1...1...1....1....1.....1.....1......1......1.......1

.1..1..1..2..3..5...8..13..21...34...55....89...144....233....377.....610

.1..1..1..2..3..5...8..13..21...34...55....89...144....233....377.....610

.1..2..2..3..4..6...9..14..22...35...56....90...145....234....378.....611

.1..3..3..4..7..9..15..26..46...84..151...276...506....929...1708....3138

.1..5..5..6..9.14..24..44..81..156..306...602..1192...2370...4720....9415

.1..8..8..9.15.24..40..76.141..277..570..1171..2441...5157..10913...23193

.1.13.13.14.26.44..76.168.359..792.1895..4521.10886..26818..66131..163463

.1.21.21.22.46.81.141.359.873.2145.5971.16568.45898.131372.376833.1078872

Examples

			All solutions for n=5, k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..612

Crossrefs

Columns 2 and 3 are A000045(n-1).

Column 4 is A001611(n-1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1).

k=2: a(n) = a(n-1) +a(n-2) for n>3.

k=3: a(n) = a(n-1) +a(n-2) for n>3.

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

k=5: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-5) -a(n-6) -a(n-7) -a(n-8) for n>9.

k=6: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) -a(n-7) +2*a(n-8) for n>9.

k=7: [order 14] for n>15.