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

1,1

Comments

Column 1 of A231324.

Links

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

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)

Example

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

Crossrefs

Cf. A231324.

Sequence in context: A320944 A277985 A091097 * A223105 A112675 A052583

Adjacent sequences: A231314 A231315 A231316 * A231318 A231319 A231320

Keyword

nonn

Author

R. H. Hardin, Nov 07 2013

Status

approved