

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
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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(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) 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



