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A198638 Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors. 1
4, 36, 376, 3936, 41216, 431616, 4519936, 47333376, 495681536, 5190844416, 54359228416, 569257230336, 5961339109376, 62427953627136, 653754017775616, 6846200955273216, 71694347178868736, 750792950862053376 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 1 of A198642.
LINKS
FORMULA
Empirical: a(n) = 12*a(n-1) -16*a(n-2) for n>3.
Conjectures from Colin Barker, May 15 2018: (Start)
G.f.: 4*x*(1 - x)*(1 - 2*x) / (1 - 12*x + 16*x^2).
a(n) = ((6 - 2*sqrt(5))^n*(-5+3*sqrt(5)) + (2*(3+sqrt(5)))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>1.
(End)
EXAMPLE
Some solutions for n=3:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....1..2....1..0....1..2....2..0....2..0....1..0....2..0....1..2....2..0
..0..2....2..0....2..1....0..1....0..1....0..1....2..1....1..2....0..1....1..2
..2..0....0..2....0..2....2..2....1..2....1..2....1..2....2..1....1..2....0..1
..1..1....2..0....2..0....2..2....2..0....2..1....0..1....0..2....2..1....1..0
..1..1....1..2....0..2....1..0....0..1....1..2....2..0....2..0....0..2....0..2
CROSSREFS
Cf. A198642.
Sequence in context: A163455 A138736 A266093 * A358954 A019999 A291274
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 27 2011
STATUS
approved

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Last modified February 23 09:02 EST 2024. Contains 370276 sequences. (Running on oeis4.)