A200872 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.

10, 37, 94, 195, 356, 595, 932, 1389, 1990, 2761, 3730, 4927, 6384, 8135, 10216, 12665, 15522, 18829, 22630, 26971, 31900, 37467, 43724, 50725, 58526, 67185, 76762, 87319, 98920, 111631, 125520, 140657, 157114, 174965, 194286, 215155, 237652, 261859

Offset

1,1

Comments

Row 2 of A200871.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 + (3/2)*n^3 + (47/12)*n^2 + (7/2)*n + 1.

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

G.f.: x*(10 - 13*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Sequence in context: A247792 A096000 A047672 * A212755 A048480 A116970

Adjacent sequences: A200869 A200870 A200871 * A200873 A200874 A200875

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved