A231045 Number of n X 4 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.

0, 32, 128, 2080, 18688, 209440, 2150784, 22847008, 239510016, 2523778080, 26540458624, 279321664544, 2938791541504, 30923196075552, 325371816285056, 3423602175951392, 36023310011880448, 379040068394055712

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*a(n-1) + 33*a(n-2) - 68*a(n-3).

Empirical g.f.: 32*x^2*(1 - 4*x) / (1 - 8*x - 33*x^2 + 68*x^3). - Colin Barker, Sep 25 2018

Example

Some solutions for n=4:
..0..1..2..3....0..3..2..3....0..3..0..1....0..3..2..3....0..3..2..1
..0..3..0..3....2..1..0..3....2..1..2..3....0..1..0..3....0..1..0..1
..2..3..2..1....0..1..2..3....2..3..0..1....0..1..2..1....2..3..0..3
..0..1..0..3....2..3..0..3....0..1..2..1....2..3..0..3....0..1..2..1

Crossrefs

Column 4 of A231049.

Sequence in context: A091905 A100626 A330818 * A031447 A153074 A035503

Adjacent sequences: A231042 A231043 A231044 * A231046 A231047 A231048

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved