A200889 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.

37, 292, 1268, 3985, 10213, 22736, 45648, 84681, 147565, 244420, 388180, 595049, 884989, 1282240, 1815872, 2520369, 3436245, 4610692, 6098260, 7961569, 10272053, 13110736, 16569040, 20749625, 25767261, 31749732, 38838772, 47191033, 56979085

Offset

1,1

Comments

Row 4 of A200886.

Links

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

Formula

Empirical: a(n) = (2/45)*n^6 + (19/15)*n^5 + (217/36)*n^4 + (71/6)*n^3 + (2057/180)*n^2 + (27/5)*n + 1.

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

G.f.: x*(37 + 33*x + x^2 - 54*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=3
..1....0....3....0....2....2....1....0....1....3....2....3....2....2....3....2
..0....1....1....3....1....3....1....0....1....0....2....3....3....1....1....2
..1....2....0....3....3....3....2....0....0....1....1....0....3....0....3....2
..3....2....1....0....3....2....2....1....1....2....0....0....1....0....3....2
..3....2....2....0....1....2....3....2....2....2....1....2....0....2....2....1
..3....3....2....3....1....0....3....2....2....1....2....2....3....3....2....0

Crossrefs

Sequence in context: A165381 A086840 A190418 * A211156 A217642 A197340

Adjacent sequences: A200886 A200887 A200888 * A200890 A200891 A200892

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved