A303525 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 18, 10, 16, 13, 31, 37, 39, 21, 32, 21, 113, 80, 103, 95, 42, 64, 34, 363, 286, 359, 340, 246, 86, 128, 55, 813, 916, 1875, 1758, 1115, 687, 179, 256, 89, 1751, 2532, 8676, 13031, 9225, 4112, 2023, 370, 512, 144, 5001, 7477, 36072

Offset

1,2

Comments

Table starts

...1...2....3.....5.......8........13.........21...........34............55

...2...3...11....21......31.......113........363..........813..........1751

...4...6...18....37......80.......286........916.........2532..........7477

...8..10...39...103.....359......1875.......8676........36072........166784

..16..21...95...340....1758.....13031......87730.......569770.......4036330

..32..42..246..1115....9225....102779....1052163.....10663440.....122173279

..64..86..687..4112...56046....965150...15768709....258412452....4730074082

.128.179.2023.16640..366415...9961980..260078546...6835357512..199276300520

.256.370.6126.71025.2519399.109395622.4544413190.190464446456.8858057538977

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

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: [order 12] for n>15

k=4: [order 47] for n>49

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6

n=3: [order 20] for n>21

n=4: [order 58] for n>60

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302310.

Sequence in context: A302309 A303040 A302877 * A368643 A133948 A078935

Adjacent sequences: A303522 A303523 A303524 * A303526 A303527 A303528

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 25 2018

Status

approved