A255625 Number of length n+3 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.

81, 243, 729, 2040, 5088, 11386, 23298, 44361, 79692, 136494, 224676, 357603, 552993, 833979, 1230355, 1780026, 2530683, 3541725, 4886451, 6654546, 8954886, 11918688, 15703032, 20494783, 26514942, 34023456, 43324518, 54772389, 68777775

Offset

1,1

Comments

Row 3 of A255622.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/672)*n^7 + (29/960)*n^6 + (39/80)*n^5 + (2463/640)*n^4 + (1/32)*n^3 + (112103/10080)*n^2 + (44923/840)*n + 12.

Empirical g.f.: x*(81 - 486*x + 1458*x^2 - 2577*x^3 + 2766*x^4 - 1790*x^5 + 672*x^6 - 135*x^7 + 12*x^8) / (1 - x)^9. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A255622.

Sequence in context: A211690 A205055 A335843 * A205048 A008876 A031456

Adjacent sequences: A255622 A255623 A255624 * A255626 A255627 A255628

Keyword

nonn

Author

R. H. Hardin, Feb 28 2015

Status

approved