A255996 Number of length n+5 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

64, 128, 188, 256, 337, 428, 530, 644, 771, 912, 1068, 1240, 1429, 1636, 1862, 2108, 2375, 2664, 2976, 3312, 3673, 4060, 4474, 4916, 5387, 5888, 6420, 6984, 7581, 8212, 8878, 9580, 10319, 11096, 11912, 12768, 13665, 14604, 15586, 16612, 17683, 18800

Offset

1,1

Comments

Row 5 of A255992.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + (5/2)*n^2 + (145/3)*n + 12 for n>3.

Empirical g.f.: x*(64 - 128*x + 60*x^2 + 16*x^3 - 7*x^4 - 8*x^5 + 4*x^6) / (1 - x)^4. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A215558 A324487 A258001 * A296166 A355265 A044187

Adjacent sequences: A255993 A255994 A255995 * A255997 A255998 A255999

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved