A255626 Number of length n+4 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.

243, 729, 2187, 5997, 14381, 30816, 60390, 110270, 190269, 313527, 497322, 764028, 1142238, 1668071, 2386683, 3354003, 4638716, 6324516, 8512653, 11324799, 14906259, 19429554, 25098404, 32152140, 40870575, 51579365, 64655892, 80535702

Offset

1,1

Comments

Row 4 of A255622.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (17/10080)*n^7 + (119/2880)*n^6 + (871/720)*n^5 + (71047/5760)*n^4 + (3599/1440)*n^3 + (56139/1120)*n^2 + (27661/280)*n + 45 for n>2.

Empirical g.f.: x*(243 - 1458*x + 4374*x^2 - 7854*x^3 + 8522*x^4 - 5193*x^5 + 1134*x^6 + 680*x^7 - 630*x^8 + 210*x^9 - 27*x^10) / (1 - x)^9. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A255622.

Sequence in context: A255111 A353320 A331613 * A205049 A235540 A219132

Adjacent sequences: A255623 A255624 A255625 * A255627 A255628 A255629

Keyword

nonn

Author

R. H. Hardin, Feb 28 2015

Status

approved