A208717 Number of n-bead necklaces labeled with numbers 1..4 allowing reversal, with no adjacent beads differing by more than 1.

4, 7, 10, 18, 28, 56, 98, 208, 418, 933, 2044, 4777, 11072, 26548, 63672, 155248, 379348, 935278, 2311294, 5741228, 14292966, 35699049, 89339860, 224097602, 563074848, 1417313897, 3572747650, 9019154944, 22797181996, 57693378135, 146168107034, 370712004868

Offset

1,1

Links

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

Formula

a(2n+1) = (1/2) * (A208773(2n+1) + A126358(n+1)). - Andrew Howroyd, Mar 03 2017

a(2n) = (1/2) * A208773(2n) + (1/4) * (A126358(n) + A126358(n+1)). - Andrew Howroyd, Mar 03 2017

Example

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

Crossrefs

Column 4 of A208721.

Cf. A208773, A126358.

Sequence in context: A310718 A310719 A103408 * A208773 A088408 A027752

Adjacent sequences: A208714 A208715 A208716 * A208718 A208719 A208720

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

a(29)-a(32) from Andrew Howroyd, Mar 03 2017

Status

approved