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

Author

R. H. Hardin, Mar 01 2012

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 5 of A208721.

Cf. A208774, A057960.

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

Extensions

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