A200835 Number of 0..5 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

176, 846, 4108, 19930, 96690, 469116, 2276028, 11042700, 53576350, 259938722, 1261156090, 6118806300, 29686880836, 144033141554, 698811908924, 3390456382404, 16449625906804, 79809371351400, 387214626739458

Offset

1,1

Comments

Column 5 of A200838.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -6*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7).

Empirical g.f.: 2*x*(88 - 105*x + 44*x^2 - 85*x^3 + 50*x^4 - 33*x^5 + 18*x^6) / (1 - 6*x + 6*x^2 - 3*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7). - Colin Barker, Oct 14 2017

Example

Some solutions for n=3
..3....5....0....4....2....3....2....5....3....1....2....0....0....4....1....3
..3....4....3....1....1....5....0....1....0....1....3....5....2....5....4....4
..0....4....0....1....5....3....4....2....5....1....3....4....1....0....4....0
..0....0....2....4....0....3....2....2....4....3....1....5....1....4....4....0
..1....1....1....2....0....5....3....2....4....3....1....5....2....0....0....5

Crossrefs

Sequence in context: A336026 A063344 A075291 * A133063 A264892 A223611

Adjacent sequences: A200832 A200833 A200834 * A200836 A200837 A200838

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved