A200840 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases.

32, 191, 676, 1817, 4108, 8239, 15128, 25953, 42184, 65615, 98396, 143065, 202580, 280351, 380272, 506753, 664752, 859807, 1098068, 1386329, 1732060, 2143439, 2629384, 3199585, 3864536, 4635567, 5524876, 6545561, 7711652, 9038143

Offset

1,1

Comments

Row 3 of A200838.

Links

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

Formula

Empirical: a(n) = (4/15)*n^5 + (17/6)*n^4 + (28/3)*n^3 + (73/6)*n^2 + (32/5)*n + 1.

Conjectures from Colin Barker, Oct 14 2017: (Start)

G.f.: x*(32 - x + 10*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Sequence in context: A306058 A317236 A233387 * A208925 A212863 A019560

Adjacent sequences: A200837 A200838 A200839 * A200841 A200842 A200843

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved