A208719 Number of n-bead necklaces labeled with numbers 1..6 allowing reversal, with no adjacent beads differing by more than 1.

6, 11, 16, 30, 48, 100, 182, 404, 850, 1996, 4614, 11391, 28002, 71236, 181710, 471437, 1227712, 3226816, 8509930, 22564205, 60002088, 160113626, 428273964, 1148410792, 3085474406, 8305718893, 22394409228, 60474491712, 163531569910, 442782412569

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Formula

a(2n+1) = (1/2) * (A208775(2n+1) + A126360(n+1)). - Andrew Howroyd, Mar 03 2017

a(2n) = (1/2) * A208775(2n) + (1/4) * (A126360(n) + A126360(n+1)). - Andrew Howroyd, Mar 03 2017

Example

All solutions for n=3:
..1....5....2....4....5....1....4....1....6....5....3....3....3....4....2....2
..2....5....3....4....5....1....5....1....6....6....3....3....4....4....2....2
..2....5....3....4....6....2....5....1....6....6....3....4....4....5....2....3

Crossrefs

Column 6 of A208721.

Cf. A208775, A126360.

Sequence in context: A315505 A333533 A191158 * A208775 A242916 A256429

Adjacent sequences: A208716 A208717 A208718 * A208720 A208721 A208722

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

a(26)-a(30) from Andrew Howroyd, Mar 03 2017

Status

approved