A275138 Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

4, 48, 224, 1088, 5248, 25344, 122368, 590848, 2852864, 13774848, 66510848, 321142784, 1550614528, 7487029248, 36150575104, 174550417408, 842803970048, 4069417549824, 19648886079488, 94873214517248, 458088402386944

Offset: 1

Author

R. H. Hardin, Jul 17 2016

Keywords

• nonn

Examples

			Some solutions for n=5:
..0..1..2..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..2..0
..2..0..1..2. .0..2..1..0. .0..1..2..0. .2..1..2..0. .2..1..2..0
..1..2..1..2. .1..0..2..0. .1..2..1..2. .2..0..1..2. .1..0..1..0
..0..2..0..1. .1..0..2..1. .1..0..2..0. .0..1..0..2. .0..2..0..2
..1..0..2..0. .2..1..0..2. .2..1..0..1. .1..2..1..2. .2..1..2..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 4 of A275142.

Formula

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

Conjectures from Colin Barker, Jan 31 2019: (Start)

G.f.: 4*x*(1 + 8*x + 4*x^2) / (1 - 4*x - 4*x^2).

a(n) = 2*((2-2*sqrt(2))^n + (2*(1+sqrt(2)))^n) for n>1.

(End)