A208666 Number of 2n-bead necklaces labeled with numbers 1..n allowing reversal, with neighbors differing by exactly 1.

0, 1, 4, 14, 44, 152, 514, 1866, 6884, 26137, 100442, 390592, 1526272, 5989223, 23548688, 92727898, 365445200, 1441195226, 5686268314, 22444465311, 88622259788, 350040069245, 1383007946774, 5465854718664, 21607909105528, 85444555330132, 337962745845558, 1337094537703089

Offset

1,3

Links

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

Formula

a(n) = (2*A208722(n) + A220062(n+1,n))/4. - Andrew Howroyd, Mar 19 2017

Example

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

Crossrefs

Diagonal of A208671.

Sequence in context: A083377 A047115 A356726 * A125068 A184138 A318019

Adjacent sequences: A208663 A208664 A208665 * A208667 A208668 A208669

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Extensions

a(11)-a(28) from Andrew Howroyd, Mar 19 2017

Status

approved