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A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases. 1
128, 1465, 8210, 31677, 96690, 250913, 577660, 1212729, 2365804, 4346969, 7598878, 12735125, 20585358, 32247681, 49148888, 73113073, 106439160, 151987897, 213278858, 294597997, 401116298, 539020065, 715653396, 939673385, 1221218596 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 5 of A200838.

LINKS

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

FORMULA

Empirical: a(n) = (34/315)*n^7 + (163/90)*n^6 + (1981/180)*n^5 + (557/18)*n^4 + (7807/180)*n^3 + (1361/45)*n^2 + (333/35)*n + 1.

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

G.f.: x*(128 + 441*x + 74*x^2 - 151*x^3 + 74*x^4 - 29*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

EXAMPLE

Some solutions for n=3

..3....2....2....0....0....2....1....2....3....1....2....0....2....3....3....0

..1....1....2....1....1....1....0....0....3....1....0....3....0....3....0....2

..1....1....0....1....1....2....3....1....0....0....0....2....0....3....2....1

..1....2....0....0....1....0....0....0....2....1....3....2....0....2....0....2

..3....1....3....0....1....0....2....3....1....0....2....1....3....2....1....2

..1....1....3....0....3....3....1....3....2....0....3....3....1....0....1....2

..1....0....3....3....2....0....1....1....2....2....2....1....1....2....3....3

CROSSREFS

Sequence in context: A221071 A070055 A247930 * A187706 A202961 A239540

Adjacent sequences:  A200839 A200840 A200841 * A200843 A200844 A200845

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 23 2011

STATUS

approved

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Last modified September 17 11:03 EDT 2019. Contains 327129 sequences. (Running on oeis4.)