A275139 Number of n X 5 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.

8, 144, 528, 2320, 9744, 41360, 175120, 741904, 3142672, 13312656, 56393232, 238885648, 1011935760, 4286628752, 18158450704, 76920431632, 325840177168, 1380281140368, 5846964738576, 24768140094736, 104919525117456

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3) for n>4.

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

G.f.: 8*x*(1 + 15*x + 7*x^2 + x^3) / ((1 + x)*(1 - 4*x - x^2)).

a(n) = 8*(2*(-1)^n - (2*((2-sqrt(5))^n - (2+sqrt(5))^n))/sqrt(5)) for n>1.

(End)

Example

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

Crossrefs

Column 5 of A275142.

Sequence in context: A227875 A235383 A275034 * A370071 A241229 A274730

Adjacent sequences: A275136 A275137 A275138 * A275140 A275141 A275142

Keyword

nonn

Author

R. H. Hardin, Jul 17 2016

Status

approved