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.

0, 6, 48, 438, 3936, 35430, 318864, 2869782, 25828032, 232452294, 2092070640, 18828635766, 169457721888, 1525119496998, 13726075472976, 123534679256790, 1111812113311104, 10006309019799942, 90056781178199472, 810511030603795254

Offset

1,2

Links

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

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

Adjacent sequences: A231101 A231102 A231103 * A231105 A231106 A231107

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved