OFFSET
0,4
COMMENTS
Also, with a different offset, number of colored quivers in the 2-mutation class of a quiver of Dynkin type A_n. - N. J. A. Sloane, Jan 22 2013
Closed formula is given in my paper linked below. - Nikos Apostolakis, Aug 01 2018
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 290.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Nikos Apostolakis, Non-crossing trees, quadrangular dissections, ternary trees, and duality preserving bijections, arXiv:1807.11602 [math.CO], July 2018.
F. Harary, E. M. Palmer, R. C. Read, On the cell-growth problem for arbitrary polygons, computer printout, circa 1974
F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Quebec 16 (1992), no 1, 53-80.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)
Alexander Stoimenow, On the number of chord diagrams, Discr. Math. 218 (2000), 209-233. See p. 232.
Torkildsen, Hermund A., Colored quivers of type A and the cell-growth problem, J. Algebra and Applications, 12 (2013), #1250133.
FORMULA
a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi) * n^(5/2) * 2^(2*n + 3)). - Vaclav Kotesovec, Mar 13 2016
MATHEMATICA
p=4; Table[Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) +If[OddQ[n], 0, Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1}]], {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name clarified by Andrew Howroyd, Nov 20 2017
STATUS
editing