

A269673


Number of lengthn 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1.


1



4, 16, 60, 224, 820, 2976, 10700, 38224, 135780, 480176, 1691740, 5941824, 20814740, 72755776, 253836780, 884207024, 3075861700, 10687549776, 37098781820, 128668433824, 445930140660, 1544500542176, 5346546062860, 18499277662224
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OFFSET

1,1


LINKS

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


FORMULA

Empirical: a(n) = 5*a(n1)  a(n2)  15*a(n3).
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 4*x*(1  x  4*x^2) / ((1  3*x)*(1  2*x  5*x^2)).
a(n) = (20*3^n + (187*sqrt(6))*(1sqrt(6))^n + (1+sqrt(6))^n*(18+7*sqrt(6))) / 15.
(End)


EXAMPLE

Some solutions for n=9:
..3. .0. .2. .0. .2. .0. .1. .0. .1. .3. .2. .2. .1. .3. .0. .0
..1. .3. .0. .1. .0. .1. .3. .1. .3. .0. .1. .1. .3. .1. .2. .0
..0. .3. .1. .3. .0. .0. .0. .1. .2. .1. .3. .3. .0. .0. .1. .1
..2. .0. .2. .3. .1. .3. .3. .0. .0. .2. .2. .1. .3. .1. .3. .3
..3. .0. .2. .2. .3. .0. .2. .2. .0. .1. .2. .0. .0. .3. .3. .2
..3. .1. .1. .1. .1. .0. .0. .0. .1. .0. .0. .0. .0. .3. .2. .0
..0. .2. .0. .0. .0. .3. .3. .3. .1. .2. .2. .3. .3. .1. .1. .3
..0. .3. .2. .1. .2. .3. .1. .1. .0. .2. .1. .2. .2. .0. .3. .3
..3. .2. .3. .2. .1. .1. .1. .3. .1. .0. .2. .1. .1. .0. .2. .0


CROSSREFS

Column 3 of A269678.
Sequence in context: A269635 A267928 A269532 * A231896 A128650 A072335
Adjacent sequences: A269670 A269671 A269672 * A269674 A269675 A269676


KEYWORD

nonn


AUTHOR

R. H. Hardin, Mar 03 2016


STATUS

approved



