A303197 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 12, 10, 16, 13, 25, 23, 23, 21, 32, 21, 65, 43, 46, 62, 42, 64, 34, 185, 105, 97, 185, 122, 86, 128, 55, 385, 233, 283, 523, 497, 305, 179, 256, 89, 649, 479, 687, 2106, 1751, 1357, 793, 370, 512, 144, 1489, 968, 1642, 7425, 8250, 5573

Offset: 1

Author

R. H. Hardin, Apr 19 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1...2....3.....5.....8.....13......21.......34........55.........89

...2...3....9....17....25.....65.....185......385.......649.......1489

...4...6...12....23....43....105.....233......479.......968.......2146

...8..10...23....46....97....283.....687.....1642......3949......10169

..16..21...62...185...523...2106....7425....23976.....77199.....278516

..32..42..122...497..1751...8250...34801...138014....547379....2363422

..64..86..305..1357..5573..32223..164295...791150...3806973...20061588

.128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170

.256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302164.

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 7] for n>11

k=4: [order 42] for n>43

k=5: [order 33] for n>37

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: [order 18] for n>19

n=4: [order 70] for n>71