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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
OFFSET
1,1
COMMENTS
Column 1 of A231324.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 07 2013
STATUS
approved