

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
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OFFSET

1,1


COMMENTS



LINKS



FORMULA

Empirical: a(n) = 12*a(n1) 16*a(n2) for n>3.
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



KEYWORD

nonn


AUTHOR



STATUS

approved



