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A231104
Number of n X 4 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, no adjacent elements equal, and upper left element zero.
1
0, 6, 48, 438, 3936, 35430, 318864, 2869782, 25828032, 232452294, 2092070640, 18828635766, 169457721888, 1525119496998, 13726075472976, 123534679256790, 1111812113311104, 10006309019799942, 90056781178199472, 810511030603795254
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) + 9*a(n-2).
Conjectures from Colin Barker, Sep 26 2018: (Start)
G.f.: 6*x^2 / ((1 + x)*(1 - 9*x)).
a(n) = (9^n + 9) / 15 for n even.
a(n) = (9^n - 9) / 15 for n odd.
(End)
EXAMPLE
Some solutions for n=4:
..0..1..2..1....0..1..2..3....0..1..2..1....0..1..0..1....0..1..2..3
..0..3..0..2....2..3..0..3....0..3..2..1....2..3..2..1....0..3..0..1
..1..2..3..0....0..1..2..3....2..1..0..3....2..3..0..1....2..3..2..3
..1..2..1..0....0..1..0..3....2..3..2..1....2..3..2..1....2..1..0..3
CROSSREFS
Column 4 of A231108.
Sequence in context: A037184 A179075 A175916 * A085457 A188911 A364923
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 03 2013
STATUS
approved