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

1,1

Links

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

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)

Example

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

Crossrefs

Column 4 of A275142.

Sequence in context: A162673 A002287 A273335 * A273767 A292074 A274729

Adjacent sequences: A275135 A275136 A275137 * A275139 A275140 A275141

Keyword

nonn

Author

R. H. Hardin, Jul 17 2016

Status

approved