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A269613 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1. 2
3, 9, 27, 78, 222, 624, 1740, 4824, 13320, 36672, 100752, 276384, 757344, 2073600, 5674176, 15520128, 42437760, 116014080, 317100288, 866621952, 2368230912, 6471278592, 17682164736, 48313178112, 132003268608, 360658059264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A269619.

LINKS

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

FORMULA

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

Conjectures from Colin Barker, Mar 21 2018: (Start)

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

a(n) = (-3*2^n + (3-2*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(3+2*sqrt(3))) / 4.

(End)

EXAMPLE

Some solutions for n=8:

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

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

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

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

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

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

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

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

CROSSREFS

Cf. A269619.

Sequence in context: A152169 A241574 A268013 * A006810 A090401 A181137

Adjacent sequences:  A269610 A269611 A269612 * A269614 A269615 A269616

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2016

STATUS

approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)