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.

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

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 A366238 A357402

Adjacent sequences: A231100 A231101 A231102 * A231104 A231105 A231106

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved