A200875 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors or less than both neighbors.

42, 343, 1528, 4917, 12890, 29325, 60112, 113745, 201994, 340659, 550408, 857701, 1295802, 1905881, 2738208, 3853441, 5324010, 7235599, 9688728, 12800437, 16706074, 21561189, 27543536, 34855185, 43724746, 54409707, 67198888, 82415013

Offset

1,1

Comments

Row 5 of A200871.

Links

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

Formula

Empirical: a(n) = (1/2520)*n^7 + (17/180)*n^6 + (281/180)*n^5 + (64/9)*n^4 + (4927/360)*n^3 + (2303/180)*n^2 + (604/105)*n + 1.

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

G.f.: x*(42 + 7*x - 40*x^2 - 55*x^3 + 70*x^4 - 29*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Sequence in context: A190533 A190602 A134386 * A215628 A190069 A105919

Adjacent sequences: A200872 A200873 A200874 * A200876 A200877 A200878

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved