A267465 Number of length-n 0..2 arrays with no following elements larger than the first repeated value.

3, 9, 24, 62, 160, 418, 1112, 3018, 8352, 23522, 67240, 194554, 568304, 1672146, 4946808, 14692970, 43767616, 130647490, 390566216, 1168815066, 3500415888, 10488664754, 31439779864, 94264813642, 282681194720, 847808703138

Offset

1,1

Comments

Column 2 of A267471.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4).

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: x*(3 - 15*x + 21*x^2 - 7*x^3) / ((1 - x)*(1 - 2*x)^2*(1 - 3*x)).

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

(End)

Example

Some solutions for n=7:
..2....1....2....1....2....2....1....1....1....0....1....0....0....1....1....2
..1....0....1....0....1....2....2....0....1....1....2....1....1....2....2....2
..0....2....0....1....0....2....0....1....0....0....2....1....2....2....1....1
..1....2....1....0....1....0....1....2....1....1....1....0....1....2....0....1
..2....2....2....2....1....1....0....2....1....0....0....0....0....1....1....2
..2....0....1....0....0....0....2....1....1....1....0....0....1....2....2....2
..1....2....2....1....0....1....0....1....1....0....1....0....1....0....2....2

Crossrefs

Cf. A267471.

Sequence in context: A269601 A006684 A342795 * A018788 A098690 A267960

Adjacent sequences: A267462 A267463 A267464 * A267466 A267467 A267468

Keyword

nonn

Author

R. H. Hardin, Jan 15 2016

Status

approved