A215229 Number of length-6 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic "squarefree").

0, 18, 408, 2940, 12600, 40110, 105168, 240408, 496080, 945450, 1690920, 2870868, 4667208, 7313670, 11104800, 16405680, 23662368, 33413058, 46299960, 63081900, 84647640, 112029918, 146420208, 189184200, 241878000, 306265050, 384333768

Offset

1,2

Comments

Row 6 of A215228.

Links

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

Formula

Empirical: a(n) = n^6 - 6*n^4 + 5*n^3 + 5*n^2 - 5*n.

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

G.f.: 6*x^2*(3 + 47*x + 77*x^2 - 7*x^3) / (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=5:
..2....1....5....4....3....0....4....5....1....4....2....5....3....1....1....5
..0....3....2....2....1....4....1....4....2....1....3....3....4....4....4....1
..5....4....3....3....2....1....2....2....3....3....1....5....5....1....0....4
..0....5....0....2....4....5....4....0....2....2....3....0....0....5....4....2
..4....1....1....0....0....4....5....4....0....5....4....2....1....2....3....3
..1....2....3....2....5....3....2....3....5....3....5....0....5....0....5....4

Crossrefs

Cf. A215228.

Sequence in context: A298465 A260655 A318598 * A172135 A005477 A361549

Adjacent sequences: A215226 A215227 A215228 * A215230 A215231 A215232

Keyword

nonn

Author

R. H. Hardin, Aug 06 2012

Status

approved