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A221184 Number of colored quivers in the 4-mutation class of a quiver of Dynkin type A_n. 1
1, 1, 3, 19, 118, 931, 7756, 68685, 630465, 5966610, 57805410, 571178751, 5737638778, 58455577800, 602859152496, 6283968796705, 66119469155523, 701526880303315, 7498841128986109, 80696081185766970, 873654669882574580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, number of nonequivalent dissections of a polygon into n+1 hexagons by nonintersecting diagonals up to rotation. - Andrew Howroyd, Nov 20 2017

LINKS

Table of n, a(n) for n=0..20.

Hermund A. Torkildsen, Colored quivers of type A and the cell-growth problem, arXiv:1004.4512 [math.RT], 2010.

Hermund A. Torkildsen, Colored quivers of type A and the cell-growth problem, J. Algebra and Applications, 12 (2013), #1250133.

FORMULA

a(n) ~ 5^(5*n + 11/2) / (sqrt(Pi) * n^(5/2) * 2^(8*n + 27/2)). - Vaclav Kotesovec, Jun 15 2018

MATHEMATICA

u[n_, k_, r_] := r*Binomial[(k - 1)*n + r, n]/((k - 1)*n + r);

T[n_, k_] := u[n, k, 1] + (If[EvenQ[n], u[n/2, k, 1], 0] - u[n, k, 2])/2 + DivisorSum[GCD[n - 1, k], EulerPhi[#]*u[(n - 1)/#, k, k/#] &]/k;

a[n_] := T[n + 1, 6];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Jun 14 2018, after Andrew Howroyd *)

CROSSREFS

Column k=6 of A295224.

Cf. A001683, A005034, A005038.

Sequence in context: A005667 A098444 A290477 * A274852 A139176 A302443

Adjacent sequences:  A221181 A221182 A221183 * A221185 A221186 A221187

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 22 2013

EXTENSIONS

a(0)=1 and a(18)-a(20) corrected by Andrew Howroyd, Nov 20 2017

STATUS

approved

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Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)