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A231103
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, no adjacent elements equal, and upper left element zero.
1
0, 2, 8, 42, 208, 1042, 5208, 26042, 130208, 651042, 3255208, 16276042, 81380208, 406901042, 2034505208, 10172526042, 50862630208, 254313151042, 1271565755208, 6357828776042, 31789143880208, 158945719401042, 794728597005208
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) + 5*a(n-2).
Conjectures from Colin Barker, Sep 26 2018: (Start)
G.f.: 2*x^2 / ((1 + x)*(1 - 5*x)).
a(n) = (5^n + 5) / 15 for n even.
a(n) = (5^n - 5) / 15 for n odd.
(End)
EXAMPLE
Some solutions for n=4:
..0..1..0....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..2
..2..3..1....0..3..0....2..3..0....2..3..0....0..3..2....0..3..2....0..3..1
..1..2..1....2..1..0....0..1..0....0..1..0....2..0..3....2..3..2....1..2..3
..3..0..3....0..3..2....2..3..2....2..3..2....1..2..1....0..1..0....1..0..3
CROSSREFS
Column 3 of A231108.
Sequence in context: A153565 A153528 A153557 * A114204 A366238 A357402
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 03 2013
STATUS
approved