A099030 Number of tone-rows in n-tone music.

1, 3, 8, 38, 192, 1320, 10176, 91296, 908160, 9985920, 119761920, 1556847360, 21794734080, 326920043520, 5230700052480, 88921882828800, 1600593472880640, 30411275613143040, 608225502973132800, 12772735554075033600

Offset

3,2

Links

Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 08 2006, Table of n, a(n) for n = 3..38

Samuel Herman, Eirini Poimenidou, Orbits of Hamiltonian Paths and Cycles in Complete Graphs, arXiv:1905.04785 [math.CO], 2019.

H. Fripertinger, Enumeration in musical theory, Séminaire Lotharingien de Combinatoire, B26a (1991), 14 pp.

Formula

(1/4) [(n-1)!+(n-1)!! ] if n odd, (1/4) [(n-1)!+(n/2+1)(n-2)!! ] if even.

Mathematica

a[n_] := If[OddQ[n], (n-1)! + (n-1)!!, (n-1)! + (n/2 + 1)*(n-2)!!] / 4;
Table[a[n], {n, 3, 38}] (* Jean-François Alcover, Aug 01 2016 *)

Prog

(PARI) doubfact(n)=if(n<2, 1, n*doubfact(n-2));
for(n=3, 50, if(n%2==1, print1(((n-1)!+doubfact(n-1))/4, ", "), print1(((n-1)!+(n/2+1)*doubfact(n-2))/4, ", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006

Crossrefs

Apart from initial terms, same as A089066. - Ray Jerome, Feb 25 2005

Sequence in context: A219953 A286075 A089066 * A264657 A190658 A366629

Adjacent sequences: A099027 A099028 A099029 * A099031 A099032 A099033

Keyword

nonn,easy

Author

Ralf Stephan, Sep 27 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006

Status

approved