A258733 Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

256, 840, 2028, 4184, 7834, 13720, 22866, 36656, 56925, 86064, 127140, 184032, 261584, 365776, 503914, 684840, 919163, 1219512, 1600812, 2080584, 2679270, 3420584, 4331890, 5444608, 6794649, 8422880, 10375620, 12705168, 15470364

Offset: 1

Author

R. H. Hardin, Jun 08 2015

Keywords

• nonn

Examples

			Some solutions for n=4:
..3....0....0....2....3....1....1....1....1....0....0....0....3....2....0....0
..0....3....0....2....2....0....3....1....1....0....0....2....2....1....1....2
..0....3....2....2....2....1....2....2....1....0....0....2....2....2....1....3
..1....3....2....0....2....1....2....3....2....2....1....2....2....3....1....3
..2....1....0....1....3....1....2....3....0....2....1....3....2....3....0....3
..2....1....0....1....0....2....2....3....0....0....1....0....0....0....2....1
..2....3....2....3....1....2....0....1....1....0....3....2....3....3....3....2
		

Links

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

Crossrefs

Row 3 of A258730.

Formula

Empirical: a(n) = (1/5040)*n^7 + (7/720)*n^6 + (29/144)*n^5 + (305/144)*n^4 + (1027/45)*n^3 + (16267/180)*n^2 + (2425/21)*n + 24 for n>1.

Empirical g.f.: x*(256 - 1208*x + 2476*x^2 - 2856*x^3 + 2026*x^4 - 904*x^5 + 242*x^6 - 32*x^7 + x^8) / (1 - x)^8. - Colin Barker, Jan 26 2018