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A221829 Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns. 1
0, 3, 16, 73, 333, 1519, 6929, 31607, 144177, 657671, 3000001, 13684663, 62423313, 284747239, 1298889569, 5924953367, 27026987697, 123285031751, 562371183361, 2565285853303, 11701686899793, 53377862792359, 243485940162209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 2 of A221828.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) for n>4.

Conjectures from Colin Barker, Aug 11 2018: (Start)

G.f.: x^2*(3 + x - x^2) / (1 - 5*x + 2*x^2).

a(n) = (2^(-4-n)*((5-sqrt(17))^n*(-7+sqrt(17)) + (5+sqrt(17))^n*(7+sqrt(17)))) / sqrt(17) for n>2.

(End)

EXAMPLE

Some solutions for n=3:

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

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

CROSSREFS

Cf. A221828.

Sequence in context: A037098 A316170 A038602 * A004303 A335625 A317365

Adjacent sequences:  A221826 A221827 A221828 * A221830 A221831 A221832

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 26 2013

STATUS

approved

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Last modified October 22 19:03 EDT 2020. Contains 337953 sequences. (Running on oeis4.)