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A269578
Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by more than one.
1
3, 9, 27, 79, 229, 659, 1889, 5401, 15419, 43977, 125355, 357191, 1017565, 2898435, 8255201, 23510865, 66956883, 190683433, 543031707, 1546443295, 4403932917, 12541401683, 35714999425, 101707905961, 289639951179, 824825396777
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 4*a(n-3) + a(n-4).
Empirical g.f.: x*(3 - 3*x - 3*x^2 + x^3) / (1 - 4*x + 2*x^2 + 4*x^3 - x^4). - Colin Barker, Jan 24 2019
EXAMPLE
Some solutions for n=6:
..2. .2. .0. .0. .1. .0. .1. .1. .2. .2. .2. .2. .1. .1. .2. .0
..2. .1. .0. .0. .0. .0. .2. .1. .0. .1. .0. .1. .1. .0. .1. .1
..0. .2. .2. .1. .2. .1. .1. .1. .2. .1. .2. .1. .1. .0. .0. .0
..1. .0. .0. .1. .1. .2. .2. .0. .1. .1. .1. .1. .2. .1. .0. .0
..1. .2. .0. .0. .2. .1. .0. .1. .0. .0. .2. .2. .1. .0. .0. .0
..0. .2. .2. .0. .0. .1. .2. .0. .2. .0. .2. .2. .0. .2. .2. .2
CROSSREFS
Column 2 of A269583.
Sequence in context: A291020 A282087 A238440 * A026289 A027129 A077844
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved