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A280668
Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
1
4, 59, 858, 12484, 181640, 2642832, 38452768, 559481408, 8140361856, 118440917248, 1723295736320, 25073667646464, 364817712941056, 5308037322346496, 77231064216379392, 1123699197608083456
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 14*a(n-1) + 8*a(n-2).
Conjectures from Colin Barker, Feb 14 2019: (Start)
G.f.: x*(4 + 3*x) / (1 - 14*x - 8*x^2).
a(n) = ((7-sqrt(57))^n*(-11+3*sqrt(57)) + (7+sqrt(57))^n*(11+3*sqrt(57))) / (16*sqrt(57)).
(End)
EXAMPLE
Some solutions for n=4:
..0..1..1. .0..1..1. .0..1..0. .0..1..2. .0..0..1. .0..1..0. .0..1..0
..0..2..2. .0..2..1. .0..2..0. .1..0..1. .1..2..2. .1..2..0. .1..2..1
..0..1..0. .0..1..2. .0..1..1. .1..0..2. .1..0..1. .1..1..2. .2..0..2
..1..2..2. .0..1..1. .0..0..1. .2..1..2. .2..2..1. .0..2..0. .0..2..1
CROSSREFS
Column 3 of A280673.
Sequence in context: A093597 A257069 A199107 * A198508 A126754 A264820
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 07 2017
STATUS
approved