A231822 Number of n X 2 0..2 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

1, 9, 64, 439, 2992, 20382, 138852, 945923, 6444056, 43899870, 299066137, 2037376372, 13879547189, 94553875250, 644144597665, 4388210021417, 29894510123024, 203655187692590, 1387393046555052, 9451561177738998

Offset

1,2

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 16*a(n-2) + 11*a(n-3) - 27*a(n-4) + 21*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(1 - x^2 - 4*x^3 - 7*x^4 - 4*x^5) / (1 - 9*x + 16*x^2 - 11*x^3 + 27*x^4 - 21*x^5 + 4*x^6). - Colin Barker, Oct 01 2018

Example

Some solutions for n=7:
..0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..0....0..0
..1..0....2..1....1..2....0..1....1..0....2..1....2..1....0..1....2..1....2..2
..2..2....1..2....1..1....0..2....0..2....2..1....1..1....2..1....1..2....2..0
..2..0....1..2....1..1....1..2....2..2....1..0....0..2....1..2....1..1....1..1
..1..0....0..1....2..2....1..0....2..2....2..2....0..1....1..0....2..0....2..2
..2..0....0..2....0..0....2..2....2..2....2..2....1..1....2..1....0..0....0..0
..2..1....1..1....0..1....0..1....2..2....0..1....2..0....0..2....1..2....1..1

Crossrefs

Column 2 of A231828.

Sequence in context: A083328 A000846 A357649 * A049684 A037540 A037484

Adjacent sequences: A231819 A231820 A231821 * A231823 A231824 A231825

Keyword

nonn

Author

R. H. Hardin, Nov 14 2013

Status

approved