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.

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

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