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 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 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

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