login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159557 Number of elements in the mutation class of a quiver of type D_n. 1
4, 6, 26, 80, 246, 810, 2704, 9252, 32066, 112720, 400024, 1432860, 5170604, 18784170, 68635478, 252088496, 930138522, 3446167860, 12815663844, 47820447028, 178987624514, 671825133648, 2528212128776, 9536895064400 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Table 1, p. 15 of Buan et al.

Except for a(4) = 6 the same as A003239. - Joerg Arndt, Aug 04 2014

LINKS

Table of n, a(n) for n=3..26.

Bakke Buan, Hermund André Torkildsen, The number of elements in the mutation class of a quiver of type $D_n$, arXiv:0812.2240 [math.RT], (14-April-2009)

FORMULA

a(n) = 6 if n = 4; otherwise a(n) = SUM[d|n] (phi(n/d))C(2d,d)/(2n) where phi is the Euler function, when n>4.

For n>4 a(n) = SUM[d|n] A000010(n/d)*A000984(d)/(2*n)

MAPLE

A159557 := proc(n) if n = 3 then 4; elif n = 4 then 6; else add( numtheory[phi](n/d)*binomial(2*d, d), d=numtheory[divisors](n))/2/n ; fi; end: seq(A159557(n), n=3..40) ; # R. J. Mathar, Apr 16 2009

MATHEMATICA

a[4] = 6; a[n_] := Sum[EulerPhi[n/d]*Binomial[2d, d]/(2n), {d, Divisors[n]} ];

Table[a[n], {n, 3, 26}] (* Jean-François Alcover, Nov 28 2017 *)

CROSSREFS

Cf. A000010, A000984.

Sequence in context: A024471 A075277 A192874 * A176756 A054094 A123873

Adjacent sequences: A159554 A159555 A159556 * A159558 A159559 A159560

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Apr 15 2009

EXTENSIONS

More terms from R. J. Mathar, Apr 16 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 12:26 EST 2022. Contains 358468 sequences. (Running on oeis4.)