A268451 Number of length-n 0..2 arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

3, 9, 25, 67, 176, 456, 1169, 2971, 7496, 18796, 46880, 116386, 287775, 709005, 1741247, 4264131, 10415559, 25381773, 61721980, 149801330, 362926749, 877831299, 2120050410, 5112962906, 12314976142, 29625637490, 71188510125

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 14*a(n-3) - 10*a(n-4) + 4*a(n-5) - a(n-6).

Empirical g.f.: x*(3 - 9*x + 10*x^2 - 8*x^3 + 3*x^4 - x^5) / (1 - 3*x + 2*x^2 - x^3)^2. - Colin Barker, Jan 13 2019

Example

Some solutions for n=9:
..1....0....0....2....2....1....0....2....1....1....2....0....1....0....1....0
..2....0....1....2....2....1....0....2....0....1....0....0....1....2....0....2
..0....2....2....1....2....2....2....1....2....2....2....1....1....2....1....0
..2....1....2....2....2....0....0....0....2....2....2....1....1....2....1....1
..2....1....2....0....2....0....2....1....1....0....2....1....1....2....2....2
..0....1....0....0....0....2....0....1....0....1....2....2....1....2....2....0
..1....0....0....0....0....0....0....1....0....2....0....2....0....1....0....2
..2....1....1....2....0....0....2....2....0....0....0....2....0....0....0....0
..2....2....1....2....0....2....1....0....2....1....1....2....2....0....1....0

Crossrefs

Column 2 of A268457.

Sequence in context: A181383 A106514 A325915 * A156561 A085327 A069403

Adjacent sequences: A268448 A268449 A268450 * A268452 A268453 A268454

Keyword

nonn

Author

R. H. Hardin, Feb 04 2016

Status

approved