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A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors. 1
114, 1691, 11472, 50995, 173606, 491533, 1215616, 2710413, 5567530, 10700151, 19461872, 33793071, 56398174, 90957305, 142375936, 217076281, 323334306, 471666355, 675269520, 950520011, 1317533910, 1800794821, 2429853056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 6 of A200886.

LINKS

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

FORMULA

Empirical: a(n) = (1/315)*n^8 + (134/315)*n^7 + (21/5)*n^6 + (571/36)*n^5 + (1841/60)*n^4 + (6047/180)*n^3 + (26603/1260)*n^2 + (299/42)*n + 1.

Conjectures from Colin Barker, Oct 16 2017: (Start)

G.f.: x*(114 + 665*x + 357*x^2 - 953*x^3 - 37*x^4 - 47*x^5 + 37*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

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

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

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

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

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

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

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

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

CROSSREFS

Sequence in context: A108344 A200551 A230464 * A240386 A220332 A162675

Adjacent sequences:  A200888 A200889 A200890 * A200892 A200893 A200894

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified May 17 08:05 EDT 2022. Contains 353741 sequences. (Running on oeis4.)