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

Author

Petros Hadjicostas, Oct 10 2017

Keywords

• nonn

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.

Examples

			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)}.)
		

Links

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

Crossrefs

Cf. A106369, A291941, A292200.

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.