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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Sequence in context: A301765 A036811 A330265 * A302635 A302427 A303197

Adjacent sequences: A302160 A302161 A302162 * A302164 A302165 A302166

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 02 2018

Status

approved