A255102 Number of length n+3 0..2 arrays with at most one downstep in every 3 consecutive neighbor pairs.

66, 168, 441, 1137, 2907, 7498, 19338, 49698, 127871, 329325, 847491, 2180700, 5613144, 14447250, 37180603, 95692059, 246288681, 633868172, 1631378124, 4198705332, 10806224445, 27811942767, 71579710341, 184225016494

Offset: 1

Author

R. H. Hardin, Feb 14 2015

Keywords

• nonn

Comments

Column 3 of A255107.

Examples

			Some solutions for n=4:
..0....2....0....2....2....1....0....0....0....2....2....0....0....0....0....2
..1....1....2....1....0....1....2....1....2....2....0....0....1....1....0....0
..0....1....0....1....1....1....0....0....2....2....0....0....1....2....0....0
..2....1....0....1....2....2....1....0....2....2....1....1....0....0....1....1
..2....2....1....1....1....2....1....2....2....2....1....2....0....0....2....0
..1....1....1....1....1....0....0....2....2....2....1....1....0....2....1....0
..2....2....0....0....2....2....1....1....1....1....1....1....1....2....2....1
		

Links

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

Crossrefs

Cf. A255107.

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +8*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6).

Empirical g.f.: x*(66 - 30*x + 135*x^2 - 210*x^3 + 69*x^4 - 26*x^5) / ((1 - x)*(1 - 2*x + x^2 - 7*x^3 + 2*x^4 - x^5)). - Colin Barker, Jan 24 2018