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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. 2
6, 24, 216, 1536, 11616, 86400, 645504, 4816896, 35956224, 268376064, 2003195904, 14952038400, 111603572736, 833020329984, 6217748545536, 46409906651136, 346408259813376, 2585626450329600, 19299378566529024, 144052522724622336 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 18 18:06 EDT 2021. Contains 345120 sequences. (Running on oeis4.)