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A200839 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 19:08 EDT 2018. Contains 316427 sequences. (Running on oeis4.)