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

Author

R. H. Hardin, Mar 13 2015

Keywords

• nonn

Comments

Row 7 of A255992.

Examples

			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
		

Links

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

Crossrefs

Cf. A255992.

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