A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.

114, 1691, 11472, 50995, 173606, 491533, 1215616, 2710413, 5567530, 10700151, 19461872, 33793071, 56398174, 90957305, 142375936, 217076281, 323334306, 471666355, 675269520, 950520011, 1317533910, 1800794821, 2429853056

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