A255112 Number of length n+5 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

729, 1791, 2907, 4429, 6582, 9297, 12662, 16779, 21765, 27753, 34893, 43353, 53320, 65001, 78624, 94439, 112719, 133761, 157887, 185445, 216810, 252385, 292602, 337923, 388841, 445881, 509601, 580593, 659484, 746937, 843652, 950367, 1067859

Offset

1,1

Comments

Row 5 of A255107.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/3)*n^4 + (115/24)*n^3 + (889/6)*n^2 + (3867/10)*n + 111 for n>3.

Empirical g.f.: x*(729 - 2583*x + 3096*x^2 - 728*x^3 - 1272*x^4 + 591*x^5 + 618*x^6 - 594*x^7 + 144*x^8) / (1 - x)^6. - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255107.

Sequence in context: A043455 A267697 A232925 * A255627 A139308 A295024

Adjacent sequences: A255109 A255110 A255111 * A255113 A255114 A255115

Keyword

nonn

Author

R. H. Hardin, Feb 14 2015

Status

approved