A200877 Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors or less than both neighbors.

110, 1523, 9858, 42479, 141688, 395929, 971416, 2156867, 4424298, 8509105, 15512938, 27033149, 45322876, 73486107, 115712352, 177555837, 266264422, 391163735, 564102306, 799963779, 1117252576, 1538759685, 2092315544

Offset

1,1

Comments

Row 7 of A200871.

Links

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

Formula

Empirical: a(n) = (1/181440)*n^9 + (131/20160)*n^8 + (8893/30240)*n^7 + (4621/1440)*n^6 + (118933/8640)*n^5 + (83957/2880)*n^4 + (763489/22680)*n^3 + (36343/1680)*n^2 + (9169/1260)*n + 1.

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

G.f.: x*(110 + 423*x - 422*x^2 - 766*x^3 + 848*x^4 - 246*x^5 + 90*x^6 - 44*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Sequence in context: A231967 A232339 A358256 * A205348 A008450 A163729

Adjacent sequences: A200874 A200875 A200876 * A200878 A200879 A200880

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved