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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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 A129277 A120916

Adjacent sequences:  A231100 A231101 A231102 * A231104 A231105 A231106

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 03 2013

STATUS

approved

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Last modified September 20 12:05 EDT 2021. Contains 347586 sequences. (Running on oeis4.)