A292906 Number of dihedral Carlitz compositions of n.

1, 1, 2, 2, 3, 5, 6, 9, 14, 20, 29, 48, 69, 110, 175, 278, 441, 725, 1168, 1928, 3170, 5253, 8710, 14563, 24308, 40798, 68520, 115433, 194611, 328938, 556336, 942659, 1598539, 2714379, 4612681, 7847082, 13358850, 22762311, 38810771, 66223599, 113067441, 193172332

Offset

1,3

Comments

A cyclic Carlitz composition is a composition of length greater than one where adjacent parts, including the first and the last ones, are distinct. A composition of length one is also considered cyclic and Carlitz. Assume two cyclic Carlitz compositions are considered equivalent iff one can be obtained from the other by a rotation or reversal of order. Each equivalence class obtained is called a dihedral Carlitz composition of n.

Links

Table of n, a(n) for n=1..42.

P. Hadjicostas, Cyclic, dihedral and symmetrical Carlitz compositions of a positive integer, Journal of Integer Sequences, 20 (2017), Article 17.8.5.

Formula

a(n) = (A106369(n) + A292200(n))/2.

a(n) = (2*A106369(n) + A291941(n) + 1)/4.

G.f.: (g.f. of A106369 + g.f. of A292200)/2.

Example

a(6) = 5 because n = 6 has the following dihedral Carlitz compositions: 6, 1+5, 2+4, 1+2+3, 1+2+1+2. (For example, the equivalence class for the dihedral Carlitz composition 1+2+3 is {(1,2,3),(2,3,1), (3,1,2), (3,2,1),(2,1,3),(1,3,2)}.)

Crossrefs

Cf. A106369, A291941, A292200.

Sequence in context: A143438 A004037 A291296 * A160235 A227392 A050380

Adjacent sequences: A292903 A292904 A292905 * A292907 A292908 A292909

Keyword

nonn

Author

Petros Hadjicostas, Oct 10 2017

Status

approved