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A209094 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors. 2
2, 11, 82, 612, 4568, 34096, 254496, 1899584, 14178688, 105831168, 789934592, 5896152064, 44009478144, 328491216896, 2451891822592, 18301169713152, 136601790414848, 1019609644466176, 7610469994070016, 56805321374695424 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 2 of A209100.
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 4*a(n-2) for n>3.
Conjectures from Colin Barker, Mar 07 2018: (Start)
G.f.: x*(2 - x)*(1 - 2*x) / (1 - 8*x + 4*x^2).
a(n) = ((4-2*sqrt(3))^n*(-1+sqrt(3)) + (1+sqrt(3))*(2*(2+sqrt(3)))^n) / (8*sqrt(3)) for n>1.
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..1
..1..2....1..0....1..1....1..1....1..1....1..0....1..1....1..2....2..1....2..1
..2..0....0..1....0..0....2..0....2..2....0..1....2..0....0..2....2..2....2..2
..0..2....0..1....2..0....0..1....1..1....1..2....1..0....2..0....1..2....0..0
CROSSREFS
Cf. A209100.
Sequence in context: A309417 A215654 A330677 * A293574 A322644 A243408
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 05 2012
STATUS
approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)