OFFSET
2,2
COMMENTS
This is the second column (m=2) of triangle A214306.
Each 2 part partition of n, with the parts written in nonincreasing order, defines a color signature. For a given color signature, say [p[1], p[2]], with p[1] >= p[2] >= 1, there are A213941(n,k)= A035206(n,k)*A213939(n,k) bracelets if this signature corresponds (with the order of the parts reversed) to the k-th partition of n in Abramowitz-Stegun (A-St) order. See A213941 for more details. Here all p(n,2)= A008284(n,2) = floor(n/2) partitions of n with 2 parts are considered. The color repertoire for a bracelet with n beads is [c[1], ..., c[n]].
Compare this sequence with A000029 where also single colored bracelets are included, and the color repertoire is only [c[1], c[2]] for all n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..100
FORMULA
EXAMPLE
a(5) = A213941(5,2) + A213941(5,3) = 20 + 40 = 60 from the bracelet (with colors j for c[j], j=1,2,..,5) cyclic(11112) which represents a class of order A035206(5,2) = 20 (if all 5 colors are used), cyclic(11122) and cyclic(11212) each representing also a color class of 20 members each, summing to 60 bracelets with five beads and five colors available for the two color signatures [4,1] and [3,2].
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Jul 31 2012
EXTENSIONS
a(25)-a(32) from Andrew Howroyd, Mar 25 2017
STATUS
approved