A159557 Number of elements in the mutation class of a quiver of type D_n.

4, 6, 26, 80, 246, 810, 2704, 9252, 32066, 112720, 400024, 1432860, 5170604, 18784170, 68635478, 252088496, 930138522, 3446167860, 12815663844, 47820447028, 178987624514, 671825133648, 2528212128776, 9536895064400

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: A370061 A192874 A371869 * 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