A258737 Number of length n+7 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

65536, 163020, 220854, 281136, 370510, 526672, 752180, 1038256, 1394568, 1831920, 2362442, 2999800, 3759427, 4658776, 5717596, 6958232, 8405950, 10089288, 12040434, 14295632, 16895617, 19886080, 23318164, 27248992, 31742228, 36868672

Offset: 1

Author

R. H. Hardin, Jun 08 2015

Keywords

• nonn

Comments

Row 7 of A258730.

Examples

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

Links

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

Crossrefs

Cf. A258730.

Formula

Empirical: a(n) = (1/5040)*n^7 + (11/720)*n^6 + (361/720)*n^5 + (1285/144)*n^4 + (40822/45)*n^3 + (1121411/180)*n^2 + (480457/35)*n + 7848 for n>5.

Empirical g.f.: x*(65536 - 361268*x + 751702*x^2 - 591152*x^3 - 236266*x^4 + 807960*x^5 - 664864*x^6 + 371040*x^7 - 206700*x^8 + 10940*x^9 + 117664*x^10 - 82072*x^11 + 17481*x^12) / (1 - x)^8. - Colin Barker, Jan 26 2018