A255989 Number of length n+5 0..1 arrays with at most one downstep in every 5 consecutive neighbor pairs.

42, 68, 114, 196, 337, 568, 945, 1574, 2645, 4476, 7568, 12736, 21365, 35852, 60308, 101608, 171148, 287940, 484045, 813826, 1369115, 2304172, 3877545, 6523278, 10972180, 18456064, 31049291, 52240182, 87891550, 147861804, 248739774

Offset

1,1

Comments

Column 5 of A255992.

Links

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

Formula

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

Empirical g.f.: x*(42 - 16*x + 20*x^2 + 36*x^3 + 59*x^4 - 78*x^5) / ((1 + x - x^3)*(1 - 3*x + 4*x^2 - 3*x^3)). - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A350641 A115957 A362003 * A192274 A291319 A226168

Adjacent sequences: A255986 A255987 A255988 * A255990 A255991 A255992

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved