A200839 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases.

16, 69, 194, 435, 846, 1491, 2444, 3789, 5620, 8041, 11166, 15119, 20034, 26055, 33336, 42041, 52344, 64429, 78490, 94731, 113366, 134619, 158724, 185925, 216476, 250641, 288694, 330919, 377610, 429071, 485616, 547569, 615264, 689045, 769266

Offset

1,1

Comments

Row 2 of A200838.

Links

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

Formula

Empirical: a(n) = (5/12)*n^4 + (19/6)*n^3 + (79/12)*n^2 + (29/6)*n + 1.

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

G.f.: x*(16 - 11*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Sequence in context: A299184 A299945 A211031 * A036660 A063493 A220212

Adjacent sequences: A200836 A200837 A200838 * A200840 A200841 A200842

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved