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URL: https://oeis.org/A275138

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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 17 2016
STATUS
approved