A255624 Number of length n+2 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.

27, 81, 243, 694, 1803, 4248, 9186, 18483, 35016, 63060, 108774, 180801, 290998, 455313, 694827, 1036980, 1517001, 2179563, 3080685, 4289904, 5892741, 7993486, 10718328, 14218857, 18675966, 24304182, 31356456, 40129443, 50969304, 64278063

Offset

1,1

Comments

Row 2 of A255622.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (59/2880)*n^6 + (61/360)*n^5 + (5167/5760)*n^4 + (901/1440)*n^3 + (17077/3360)*n^2 + (3977/280)*n + 6.

Empirical g.f.: x*(3 - 2*x)*(9 - 48*x + 130*x^2 - 195*x^3 + 171*x^4 - 87*x^5 + 24*x^6 - 3*x^7) / (1 - x)^9. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A255622.

Sequence in context: A216438 A292872 A057609 * A008884 A031455 A045004

Adjacent sequences: A255621 A255622 A255623 * A255625 A255626 A255627

Keyword

nonn

Author

R. H. Hardin, Feb 28 2015

Status

approved