A267226 Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.

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

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

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

Adjacent sequences: A267223 A267224 A267225 * A267227 A267228 A267229

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved