A242317 Number of length n+2+2 0..2 arrays with every value 0..2 appearing at least once in every consecutive 2+3 elements, and new values 0..2 introduced in order.

25, 61, 145, 337, 781, 1829, 4269, 9957, 23233, 54225, 126533, 295265, 689021, 1607877, 3752057, 8755625, 20431737, 47678569, 111260509, 259632437, 605866385, 1413822053, 3299230409, 7698933081, 17965877829, 41924350093, 97832744293

Offset

1,1

Comments

Column 2 of A242322.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-5) - a(n-6).

Empirical g.f.: x*(25 + 36*x + 34*x^2 + 20*x^3 - 18*x^4 - 13*x^5) / ((1 + x)*(1 - 2*x - 2*x^3 + x^5)). - Colin Barker, Mar 19 2018

Example

Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....0....1....0....0....1....1....1
..0....2....1....2....1....0....2....1....0....1....0....1....1....0....1....2
..1....2....2....0....2....1....2....2....0....2....2....1....0....2....0....0
..2....0....0....1....0....2....2....2....2....2....2....2....2....1....2....1
..1....2....2....0....2....0....0....0....1....0....1....2....2....2....1....2
..1....1....1....2....2....1....1....1....0....1....2....0....2....0....2....1
..0....1....2....2....1....1....1....0....0....2....0....1....1....2....0....2
..0....0....2....0....2....0....2....0....1....2....2....0....0....0....2....0

Crossrefs

Cf. A242322.

Sequence in context: A044127 A044508 A166873 * A251688 A211326 A103645

Adjacent sequences: A242314 A242315 A242316 * A242318 A242319 A242320

Keyword

nonn

Author

R. H. Hardin, May 10 2014

Status

approved