A255994 Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

16, 32, 53, 80, 114, 156, 207, 268, 340, 424, 521, 632, 758, 900, 1059, 1236, 1432, 1648, 1885, 2144, 2426, 2732, 3063, 3420, 3804, 4216, 4657, 5128, 5630, 6164, 6731, 7332, 7968, 8640, 9349, 10096, 10882, 11708, 12575, 13484, 14436, 15432, 16473, 17560

Offset

1,1

Comments

Row 3 of A255992.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + (3/2)*n^2 + (31/3)*n + 4.

Empirical g.f.: x*(16 - 32*x + 21*x^2 - 4*x^3) / (1 - x)^4. - Colin Barker, Jan 25 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A048946 A260050 A224544 * A204645 A236323 A018923

Adjacent sequences: A255991 A255992 A255993 * A255995 A255996 A255997

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved