A208718 Number of n-bead necklaces labeled with numbers 1..5 allowing reversal, with no adjacent beads differing by more than 1.

5, 9, 13, 24, 38, 78, 140, 306, 634, 1464, 3326, 8066, 19454, 48534, 121294, 308154, 785222, 2018548, 5203634, 13482426, 35019010, 91251438, 238278314, 623629333, 1635062126, 4294493670, 11296419934, 29757590061, 78489973742, 207281830814

Offset

1,1

Links

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

Formula

a(2n+1) = (1/2) * (A208774(2n+1) + r(n+1)) where r(n) = A057960(n+1). - Andrew Howroyd, Mar 03 2017

a(2n) = (1/2) * A208774(2n) + (1/4) * (r(n) + r(n+1)) where r(n) = A057960(n+1). - Andrew Howroyd, Mar 03 2017

Example

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

Crossrefs

Column 5 of A208721.

Cf. A208774, A057960.

Sequence in context: A314796 A314797 A314798 * A208774 A271391 A151907

Adjacent sequences: A208715 A208716 A208717 * A208719 A208720 A208721

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

a(25)-a(30) from Andrew Howroyd, Mar 03 2017

Status

approved