A208720 Number of n-bead necklaces labeled with numbers 1..7 allowing reversal, with no adjacent beads differing by more than 1.

7, 13, 19, 36, 58, 122, 224, 502, 1066, 2528, 5902, 14717, 36557, 93987, 242387, 635990, 1675743, 4457771, 11903835, 31970464, 86144382, 233001926, 631920076, 1718567054, 4684178054, 12794677456, 35012475762, 95976563897, 263496604025, 724445459431

Offset

1,1

Links

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

Formula

a(2n+1) = (1/2) * (A208776(2n+1) + A002714(n+1)). - Andrew Howroyd, Mar 03 2017

a(2n) = (1/2) * A208776(2n) + (1/4) * (A002714(n) + A002714(n+1)). - Andrew Howroyd, Mar 03 2017

Example

All solutions for n=3:
..1....1....6....3....6....5....2....4....4....3....5....4....5....7....6....2
..2....1....6....4....7....5....3....4....5....3....6....4....5....7....6....2
..2....1....7....4....7....5....3....5....5....3....6....4....6....7....6....3
..
..1....2....3
..1....2....3
..2....2....4

Crossrefs

Column 7 of A208721.

Cf. A208776, A002714.

Sequence in context: A283191 A048375 A198035 * A208776 A108295 A071923

Adjacent sequences: A208717 A208718 A208719 * A208721 A208722 A208723

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

a(22)-a(30) from Andrew Howroyd, Mar 03 2017

Status

approved