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

Author

Ralf Stephan, Sep 27 2004

Keywords

• nonn
• easy

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.

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

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