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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
OFFSET
1,1
COMMENTS
Row 6 of A200871.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 23 2011
STATUS
approved