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