A255988 Number of length n+4 0..1 arrays with at most one downstep in every 4 consecutive neighbor pairs.

26, 45, 80, 144, 256, 451, 796, 1413, 2510, 4448, 7872, 13943, 24718, 43817, 77636, 137540, 243712, 431899, 765360, 1356169, 2403034, 4258172, 7545592, 13370799, 23692770, 41983189, 74394040, 131826104, 233594880, 413927683, 733476228

Offset

1,1

Comments

Column 4 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) +3*a(n-4) -2*a(n-5).

Empirical g.f.: x*(26 - 7*x + 16*x^2 + 29*x^3 - 30*x^4) / (1 - 2*x + x^2 - 3*x^4 + 2*x^5). - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A260200 A178100 A357569 * A304673 A039458 A291672

Adjacent sequences: A255985 A255986 A255987 * A255989 A255990 A255991

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved