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A200876 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors or less than both neighbors. 1
68, 723, 3882, 14455, 42744, 107777, 241718, 495495, 945790, 1703537, 2924076, 4819113, 7670638, 11846955, 17820980, 26190965, 37703808, 53281111, 74048150, 101365923, 136866444, 182491453, 240534714, 313688075, 405091466, 518387013 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 6 of A200871.

LINKS

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

FORMULA

Empirical: a(n) = (1/20160)*n^8 + (19/720)*n^7 + (211/288)*n^6 + (1889/360)*n^5 + (44167/2880)*n^4 + (15991/720)*n^3 + (5689/336)*n^2 + (391/60)*n + 1.

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

G.f.: x*(68 + 111*x - 177*x^2 - 167*x^3 + 237*x^4 - 97*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

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

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

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

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

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

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

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

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

CROSSREFS

Sequence in context: A282333 A244440 A166398 * A039507 A250144 A250338

Adjacent sequences:  A200873 A200874 A200875 * A200877 A200878 A200879

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified July 7 11:56 EDT 2022. Contains 355148 sequences. (Running on oeis4.)