A302163 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 7, 10, 16, 13, 25, 12, 17, 21, 32, 21, 65, 20, 29, 31, 42, 64, 34, 185, 34, 51, 73, 57, 86, 128, 55, 385, 56, 109, 140, 156, 111, 179, 256, 89, 649, 94, 206, 296, 280, 361, 265, 370, 512, 144, 1489, 156, 407, 603, 635, 621, 865, 527, 770

Offset: 1

Author

R. H. Hardin, Apr 02 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

...2...3...9...17...25...65...185...385...649...1489...3929....8609...15913

...4...6...7...12...20...34....56....94...156....262....436.....730....1216

...8..10..17...29...51..109...206...407...791...1584...3104....6165...12131

..16..21..31...73..140..296...603..1288..2584...5456..11189...23561...48423

..32..42..57..156..280..635..1247..2815..5524..12457..25230...55645..113410

..64..86.111..361..621.1563..2853..7306.12963..33522..61775..157788..293072

.128.179.265..865.1451.3948..6870.19993.32005.100147.163475..531350..820788

.256.370.527.1970.3189.9405.15489.50691.75825.282597.409385.1667452.2263018

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..720

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +8*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7) for n>11

k=4: [order 15] for n>19

k=5: [order 12] for n>15

k=6: [order 15] for n>26

k=7: [order 27] for n>39

Empirical for row n:

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

n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

n=3: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) for n>6

n=4: [order 22] for n>23

n=5: [order 36] for n>40

n=6: [order 35] for n>45

n=7: [order 80] for n>89