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A267226
Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.
1
3, 9, 21, 47, 103, 223, 479, 1023, 2175, 4607, 9727, 20479, 43007, 90111, 188415, 393215, 819199, 1703935, 3538943, 7340031, 15204351, 31457279, 65011711, 134217727, 276824063, 570425343, 1174405119, 2415919103, 4966055935
OFFSET
1,1
COMMENTS
Column 2 of A267232.
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(3 - 6*x + 2*x^3) / ((1 - x)*(1 - 2*x)^2).
a(n) = 2^(n+1) + 2^(n-2)*n - 1 for n>1.
(End)
EXAMPLE
Some solutions for n=6:
1 0 0 1 2 0 1 2 1 1 0 2 1 1 2 2
0 2 1 2 0 2 2 1 0 2 2 1 2 0 0 1
2 2 2 0 1 0 1 2 1 1 0 0 0 2 2 0
0 0 0 2 2 1 2 0 0 2 1 1 2 2 2 1
2 0 2 1 1 1 0 2 1 1 0 1 0 1 1 2
1 1 1 1 0 0 1 1 1 1 2 0 1 1 0 0
CROSSREFS
Cf. A267232.
Sequence in context: A262197 A014286 A000714 * A273845 A090984 A319781
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 12 2016
STATUS
approved