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

1,1

Comments

Row 7 of A258730.

Links

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

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

Example

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

Crossrefs

Cf. A258730.

Sequence in context: A202939 A069277 A202932 * A255667 A242323 A016784

Adjacent sequences: A258734 A258735 A258736 * A258738 A258739 A258740

Keyword

nonn

Author

R. H. Hardin, Jun 08 2015

Status

approved