A215230 Number of length-7 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic "squarefree").

0, 0, 840, 10080, 57960, 228480, 710640, 1874880, 4379760, 9313920, 18378360, 34114080, 60180120, 101687040, 165590880, 261152640, 400468320, 599074560, 876634920, 1257711840, 1772629320, 2458431360, 3359941200, 4530926400

Offset

1,3

Comments

Row 7 of A215228.

Links

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

Formula

Empirical: a(n) = n^7 - 7*n^5 + 14*n^3 - 8*n = n*(n-1)*(n-2)*(n+2)*(n+1)*(n^2-2).

Conjectures from Colin Barker, Jul 23 2018: (Start)

G.f.: 840*x^3*(1 + 4*x + x^2) / (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=5:
..1....5....1....0....1....0....4....0....0....4....3....1....3....0....3....1
..2....4....3....1....0....3....0....4....5....2....0....4....5....3....2....2
..5....2....1....3....4....2....3....2....4....5....3....1....0....4....3....4
..3....4....5....1....5....3....4....5....1....4....5....2....5....5....5....0
..0....5....2....4....4....4....0....0....0....3....0....0....3....0....1....5
..5....1....5....1....3....2....5....2....4....0....3....2....0....2....2....3
..3....3....4....3....4....1....0....3....5....5....1....3....1....5....4....5

Crossrefs

Cf. A215228.

Sequence in context: A177021 A276161 A135038 * A171260 A166758 A188781

Adjacent sequences: A215227 A215228 A215229 * A215231 A215232 A215233

Keyword

nonn

Author

R. H. Hardin, Aug 06 2012

Status

approved