A256817 Number of length n+2 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

8, 16, 32, 64, 124, 229, 402, 673, 1080, 1670, 2500, 3638, 5164, 7171, 9766, 13071, 17224, 22380, 28712, 36412, 45692, 56785, 69946, 85453, 103608, 124738, 149196, 177362, 209644, 246479, 288334, 335707, 389128, 449160, 516400, 591480, 675068

Offset: 1

Author

R. H. Hardin, Apr 10 2015

Keywords

• nonn

Comments

Row 2 of A256816.

Examples

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

Links

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

Crossrefs

Cf. A256816.

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (3/8)*n^3 - (1/24)*n^2 + (277/60)*n + 3.

Empirical g.f.: x*(8 - 32*x + 56*x^2 - 48*x^3 + 20*x^4 - 3*x^5) / (1 - x)^6. - Colin Barker, Jan 21 2018