A255998 Number of length n+7 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

256, 512, 667, 796, 945, 1134, 1352, 1584, 1831, 2094, 2374, 2672, 2989, 3326, 3684, 4064, 4467, 4894, 5346, 5824, 6329, 6862, 7424, 8016, 8639, 9294, 9982, 10704, 11461, 12254, 13084, 13952, 14859, 15806, 16794, 17824, 18897, 20014, 21176, 22384, 23639

Offset

1,1

Comments

Row 7 of A255992.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + (7/2)*n^2 + (454/3)*n + 64 for n>5.

Empirical g.f.: x*(256 - 512*x + 155*x^2 + 176*x^3 - 29*x^4 - 26*x^5 - 31*x^6 - 4*x^7 + 16*x^8) / (1 - x)^4. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A206206 A206199 A271811 * A309092 A043336 A256822

Adjacent sequences: A255995 A255996 A255997 * A255999 A256000 A256001

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved