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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

R. H. Hardin, Table of n, a(n) for n = 1..200

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 * A019999 A291274 A239112

Adjacent sequences:  A198635 A198636 A198637 * A198639 A198640 A198641

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 27 2011

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)