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A221764 Number of n X 3 arrays of occupancy after each element moves to some horizontal or vertical neighbor, without 2-loops or left turns. 1
0, 3, 16, 92, 536, 3125, 18216, 106174, 618832, 3606823, 21022112, 122525856, 714133032, 4162272345, 24259501048, 141394733954, 824108902688, 4803258682187, 27995443190448, 163169400460516, 951020959572664 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A221768.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..71

FORMULA

Empirical: a(n) = 8*a(n-1) - 14*a(n-2) + 8*a(n-3) - a(n-4).

Conjectures from Colin Barker, Aug 10 2018: (Start)

G.f.: x^2*(3 - 8*x + 6*x^2) / ((1 - x)^2*(1 - 6*x + x^2)).

a(n) = (40+sqrt(2)*((81-56*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(81+56*sqrt(2))) - 8*(1+n)) / 32.

(End)

EXAMPLE

Some solutions for n=3:

..1..1..1....0..1..1....1..2..1....1..2..1....0..1..1....1..1..1....0..1..1

..2..0..1....1..2..2....1..2..1....1..1..1....1..1..2....2..1..1....1..1..1

..1..1..1....0..1..1....0..1..0....1..1..0....1..1..1....1..1..0....1..2..1

CROSSREFS

Cf. A221768.

Sequence in context: A067679 A099952 A305852 * A213229 A323968 A074555

Adjacent sequences:  A221761 A221762 A221763 * A221765 A221766 A221767

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 25 2013

STATUS

approved

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)