A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.

65, 704, 3823, 14288, 42182, 105813, 235538, 478467, 904111, 1611038, 2734601, 4455802, 7011356, 10705019, 15920244, 23134229, 32933421, 46030540, 63283187, 85714100, 114533122, 151160945, 197254694, 254735415, 325817531, 413040330

Offset

1,1

Comments

Row 5 of A200886.

Links

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

Formula

Empirical: a(n) = (4/315)*n^7 + (7/9)*n^6 + (241/45)*n^5 + (1067/72)*n^4 + (3757/180)*n^3 + (1145/72)*n^2 + (2629/420)*n + 1.

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

G.f.: x*(65 + 184*x + 11*x^2 - 224*x^3 + 48*x^4 - 27*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
..0....2....3....2....2....3....2....0....2....0....2....2....3....2....1....1
..1....3....0....2....0....2....2....3....3....3....0....0....1....2....0....2
..1....3....0....3....3....2....1....3....3....3....3....1....2....3....2....2
..0....0....2....3....3....0....2....3....3....2....3....1....2....3....2....2
..2....1....3....0....2....0....2....2....0....3....2....0....2....3....2....2
..2....1....3....0....2....2....0....0....1....3....0....1....1....3....0....0
..2....3....2....2....1....3....1....0....3....3....1....1....0....3....1....1

Crossrefs

Sequence in context: A297317 A224099 A220229 * A268265 A353939 A351269

Adjacent sequences: A200887 A200888 A200889 * A200891 A200892 A200893

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved