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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 January 21 13:54 EST 2020. Contains 331113 sequences. (Running on oeis4.)