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

Author

R. H. Hardin, Apr 25 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302310.

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