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A231280
Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.
1
0, 2, 8, 66, 400, 2722, 17688, 117026, 768800, 5064642, 33328168, 219411586, 1444225200, 9506897762, 62579419448, 411934939746, 2711589889600, 17849253534082, 117494042259528, 773413479117506, 5091052634882000
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) + 17*a(n-2).
Conjectures from Colin Barker, Sep 28 2018: (Start)
G.f.: 2*x^2 / (1 - 4*x - 17*x^2).
a(n) = ((2-sqrt(21))^n*(2+sqrt(21)) + (-2+sqrt(21))*(2+sqrt(21))^n)/(17*sqrt(21)).
(End)
EXAMPLE
Some solutions for n=3:
..0..1..0....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0
..2..3..2....0..3..0....2..3..0....2..3..0....0..3..2....2..3..2....2..3..2
..0..1..0....2..1..0....2..1..0....2..1..0....2..1..0....0..1..0....2..1..0
CROSSREFS
Column 3 of A231285.
Sequence in context: A011836 A309251 A100623 * A086594 A132219 A226730
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 06 2013
STATUS
approved