login
A215230
Number of length-7 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic "squarefree").
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 06 2012
STATUS
approved