This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A292223 a(n) is the number of representative six-color bracelets (necklaces with turning over allowed; D_6 symmetry) with n beads, for n >= 6. 0
 60, 180, 1050, 5040, 29244, 161340, 1046250, 4825800, 27790266, 145126548, 843333015, 4466836920, 26967624184, 137243187108, 789854179074, 4306147750200, 24711052977222, 134216193832908, 797987818325009, 4240082199867228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 COMMENTS This is the sixth column (m = 6) of triangle A213940. The relevant p(n,6)= A008284(n, 6) representative color multinomials have exponents (signatures) from the six-part partitions of n, written with nonincreasing parts. E.g., n = 8: [3,1,1,1,1,1] and [2,2,1,1,1,1] (p(8,6)=2). The corresponding representative bracelets have the six-color multinomials c[1]^3*c[2]*c[3]*c[4]*c[5]*c[6] and c[1]^2*c[2]^2*c[3]*c[4]*c[5]*c[6]. See A056361 for the numbers if also color permutations for D_6 inequivalent bracelets are allowed. (Andrew Howroyd induced me to look at these bracelets.) LINKS FORMULA a(n) = A213940(n, 6), n >= 6. a(n) = Sum_{k=b(n, 6)..b(n, 7)-1} A213939(n, k), for n >= 7, with b(n, m) = A214314(n, m) the position where the first m-part partition of n appears in the Abramowitz-Stegun ordering of partitions (see A036036 for the reference and a historical comment), and a(6) = A213939(6, b(6,6)) = A213939(6, 11) = 60. EXAMPLE a(6) = A213940(6,6) = A213939(6, 11) = 60 from the representative bracelets (with colors j for c(j), j=1..6) permutations of (1, 2, 3, 4, 5, 6) modulo D_6 (dihedral group) symmetry, i.e., modulo cyclic or anti-cyclic operations. E.g., (1, 2, 3, 4, 6, 5) == (2, 3, 4, 6, 5, 1) == (6, 4, 3, 2, 1, 5) == ..., but (1, 2, 3, 4, 6, 5) is not equivalent to (1, 2, 3, 4, 5, 6). If color permutation is also allowed, then there is only one possibility (see A056361(6) = 1). CROSSREFS Cf. A008284, A036036, A056361, A213940, A214311, A214314. Sequence in context: A291549 A259946 A249911 * A112827 A181333 A082529 Adjacent sequences:  A292220 A292221 A292222 * A292224 A292225 A292226 KEYWORD nonn AUTHOR Wolfdieter Lang, Sep 30 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 12:42 EDT 2018. Contains 315239 sequences. (Running on oeis4.)