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A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases. 1
256, 4057, 28610, 132263, 469116, 1384813, 3570086, 8291391, 17720746, 35389651, 66794740, 120185585, 207567842, 345957699, 558926356, 878476037, 1347291804, 2021416213, 2973396622, 4295957731, 6106254704, 8550764993, 11810879754 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 6 of A200838.

LINKS

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

FORMULA

Empirical: a(n) = (277/4032)*n^8 + (1375/1008)*n^7 + (4933/480)*n^6 + (2723/72)*n^5 + (14161/192)*n^4 + (11197/144)*n^3 + (216211/5040)*n^2 + (929/84)*n + 1.

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

G.f.: x*(256 + 1753*x + 1313*x^2 - 679*x^3 + 177*x^4 - 77*x^5 + 35*x^6 - 9*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

EXAMPLE

Some solutions for n=3

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

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

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

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

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

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

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

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

CROSSREFS

Sequence in context: A231842 A186558 A186554 * A074151 A016804 A115111

Adjacent sequences:  A200840 A200841 A200842 * A200844 A200845 A200846

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 23 2011

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)