A200874 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors or less than both neighbors.

26, 163, 602, 1673, 3886, 7973, 14932, 26073, 43066, 67991, 103390, 152321, 218414, 305929, 419816, 565777, 750330, 980875, 1265762, 1614361, 2037134, 2545709, 3152956, 3873065, 4721626, 5715711, 6873958, 8216657, 9765838, 11545361

Offset

1,1

Comments

Row 4 of A200871.

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (7/24)*n^5 + (197/72)*n^4 + (185/24)*n^3 + (1667/180)*n^2 + 5*n + 1.

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

G.f.: x*(26 - 19*x + 7*x^2 - 28*x^3 + 22*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
..2....0....2....0....2....1....2....0....3....0....0....1....3....3....1....1
..0....2....2....3....0....2....1....1....3....2....0....1....3....0....2....3
..0....2....2....3....0....2....1....3....0....3....1....1....2....0....2....3
..0....0....2....2....0....2....2....3....0....3....2....0....2....1....2....2
..0....0....1....2....1....1....2....0....2....3....2....0....3....1....2....2
..0....3....1....3....1....0....1....0....2....1....0....0....3....3....2....0

Crossrefs

Sequence in context: A232585 A042314 A280213 * A027280 A006354 A249292

Adjacent sequences: A200871 A200872 A200873 * A200875 A200876 A200877

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved