A200873 Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors or less than both neighbors.

16, 77, 236, 567, 1168, 2163, 3704, 5973, 9184, 13585, 19460, 27131, 36960, 49351, 64752, 83657, 106608, 134197, 167068, 205919, 251504, 304635, 366184, 437085, 518336, 611001, 716212, 835171, 969152, 1119503, 1287648, 1475089, 1683408

Offset

1,1

Comments

Row 3 of A200871.

Links

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

Formula

Empirical: a(n) = (1/60)*n^5 + (3/4)*n^4 + (15/4)*n^3 + (25/4)*n^2 + (127/30)*n + 1.

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

G.f.: x*(16 - 19*x + 14*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Sequence in context: A007834 A228741 A346636 * A082966 A198182 A281466

Adjacent sequences: A200870 A200871 A200872 * A200874 A200875 A200876

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved