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A032261 Number of bracelets with n labeled beads of 3 colors. 1
1, 3, 9, 27, 243, 2916, 43740, 787320, 16533720, 396809280, 10713850560, 321415516800, 10606712054400, 381841633958400, 14891823724377600, 625456596423859200, 28145546839073664000, 1350986248275535872000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. G. Bower, Transforms (2)

FORMULA

"DIJ" (bracelet, indistinct, labeled) transform of 3, 0, 0, 0, ...

a(n) = 3^n*(n-1)!/2 for n >= 3.

E.g.f.: 1 + (g(x) + g(x)^2/2 - log(1-g(x)))/2 where g(x) = 3*x. - Andrew Howroyd, Sep 12 2018

PROG

(PARI) a(n)={3^n*if(n<3, 1, (n-1)!/2)} \\ Andrew Howroyd, Sep 12 2018

(PARI) seq(n)={my(p=3*x + O(x*x^n)); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ Andrew Howroyd, Sep 12 2018

CROSSREFS

Sequence in context: A299597 A143014 A202907 * A300981 A018924 A061582

Adjacent sequences:  A032258 A032259 A032260 * A032262 A032263 A032264

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

EXTENSIONS

a(0)=1 prepended by Andrew Howroyd, Sep 12 2018

STATUS

approved

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Last modified October 19 15:39 EDT 2018. Contains 316365 sequences. (Running on oeis4.)