A231317 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

6, 24, 216, 1536, 11616, 86400, 645504, 4816896, 35956224, 268376064, 2003195904, 14952038400, 111603572736, 833020329984, 6217748545536, 46409906651136, 346408259813376, 2585626450329600, 19299378566529024, 144052522724622336

Offset: 1

Author

R. H. Hardin, Nov 07 2013

Keywords

• nonn

Comments

Column 1 of A231324.

Examples

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

Links

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

Crossrefs

Cf. A231324.

Formula

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 8*a(n-3).

Conjectures from Colin Barker, Mar 18 2018: (Start)

G.f.: 6*x*(1 - 2*x) / ((1 + 2*x)*(1 - 8*x + 4*x^2)).

a(n) = ((-2)^(1+n) + (4-2*sqrt(3))^n + (2*(2+sqrt(3)))^n) / 2.

(End)