A258735 Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

4096, 11704, 20955, 35540, 59188, 92548, 138196, 199264, 279560, 383704, 517281, 687012, 900944, 1168660, 1501510, 1912864, 2418388, 3036344, 3787915, 4697556, 5793372, 7107524, 8676664, 10542400, 12751792, 15357880, 18420245, 22005604

Offset

1,1

Comments

Row 5 of A258730.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/80)*n^6 + (241/720)*n^5 + (229/48)*n^4 + (15569/90)*n^3 + (58693/60)*n^2 + (175526/105)*n + 512 for n>3.

Empirical g.f.: x*(4096 - 21064*x + 42011*x^2 - 33764*x^3 - 7096*x^4 + 30588*x^5 - 9050*x^6- 20224*x^7 + 22372*x^8 - 9344*x^9 + 1476*x^10) / (1 - x)^8. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A258730.

Sequence in context: A069273 A043424 A138174 * A180972 A255665 A223334

Adjacent sequences: A258732 A258733 A258734 * A258736 A258737 A258738

Keyword

nonn

Author

R. H. Hardin, Jun 08 2015

Status

approved