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A208561
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 left-upward diagonal neighbors.
1
2, 10, 68, 464, 3168, 21632, 147712, 1008640, 6887424, 47030272, 321142784, 2192900096, 14974058496, 102249267200, 698201669632, 4767619219456, 32555340398592, 222301769433088, 1517971432275968, 10365357302743040
OFFSET
1,1
COMMENTS
Column 2 of A208567.
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 8*a(n-2) for n>3.
Conjectures from Colin Barker, Jul 05 2018: (Start)
G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 8*x + 8*x^2).
a(n) = ((4-2*sqrt(2))^n*(-1+sqrt(2)) + (1+sqrt(2))*(2*(2+sqrt(2)))^n) / (8*sqrt(2)) for n>1.
(End)
EXAMPLE
Some solutions for n=4:
..0..1....0..0....0..1....0..0....0..0....0..0....0..0....0..0....0..1....0..0
..1..0....1..2....0..2....1..2....0..1....1..1....1..1....0..1....2..1....0..1
..1..2....0..2....1..2....0..2....0..1....2..0....0..0....0..1....2..0....0..1
..1..2....1..0....2..1....2..0....0..1....0..1....2..1....2..1....0..1....1..2
CROSSREFS
Cf. A208567.
Sequence in context: A325995 A366178 A049036 * A152620 A152621 A147725
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 28 2012
STATUS
approved