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 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Nov 28 2017 14:10:09
%S 4,6,26,80,246,810,2704,9252,32066,112720,400024,1432860,5170604,
%T 18784170,68635478,252088496,930138522,3446167860,12815663844,
%U 47820447028,178987624514,671825133648,2528212128776,9536895064400
%N Number of elements in the mutation class of a quiver of type D_n.
%C Table 1, p. 15 of Buan et al.
%C Except for a(4) = 6 the same as A003239. - _Joerg Arndt_, Aug 04 2014
%H Bakke Buan, Hermund André Torkildsen, <a href="http://arxiv.org/abs/0812.2240">The number of elements in the mutation class of a quiver of type $D_n$</a>, arXiv:0812.2240 [math.RT], (14-April-2009)
%F 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.
%F For n>4 a(n) = SUM[d|n] A000010(n/d)*A000984(d)/(2*n)
%p 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
%t a[4] = 6; a[n_] := Sum[EulerPhi[n/d]*Binomial[2d, d]/(2n), {d, Divisors[n]} ];
%t Table[a[n], {n, 3, 26}] (* _Jean-François Alcover_, Nov 28 2017 *)
%Y Cf. A000010, A000984.
%K nonn
%O 3,1
%A _Jonathan Vos Post_, Apr 15 2009
%E More terms from _R. J. Mathar_, Apr 16 2009