A258732 Number of length n+2 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

64, 225, 608, 1408, 2936, 5664, 10280, 17754, 29416, 47047, 72984, 110240, 162640, 234974, 333168, 464474, 637680, 863341, 1154032, 1524624, 1992584, 2578300, 3305432, 4201290, 5297240, 6629139, 8237800, 10169488, 12476448, 15217466

Offset

1,1

Comments

Row 2 of A258730.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (5/4)*n^4 + (5167/720)*n^3 + (2489/120)*n^2 + (2591/105)*n + 10.

Empirical g.f.: x*(64 - 287*x + 600*x^2 - 740*x^3 + 576*x^4 - 282*x^5 + 80*x^6 - 10*x^7) / (1 - x)^8. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A258730.

Sequence in context: A295021 A194932 A016994 * A279714 A228802 A222547

Adjacent sequences: A258729 A258730 A258731 * A258733 A258734 A258735

Keyword

nonn

Author

R. H. Hardin, Jun 08 2015

Status

approved