login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085614 Elementary arches of size n. 3
1, 3, 16, 105, 768, 6006, 49152, 415701, 3604480, 31870410, 286261248, 2604681690, 23957864448, 222399744300, 2080911654912, 19604537460045, 185813170126848, 1770558814528770, 16951376923852800, 162984598242674670 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

F. Cazals, Combinatorics of Non-Crossing Configurations, Studies in Automatic Combinatorics, Volume II (1997).

Loïc Foissy, Free quadri-algebras and dual quadri-algebras, arXiv preprint arXiv:1504.06056 [math.CO], 2015.

I. M. Gessel, A short proof of the Deutsch-Sagan congruence for connected non crossing graphs, arXiv preprint arXiv:1403.7656 [math.CO], 2014.

Thomas M. Richardson, The three 'R's and Dual Riordan Arrays, arXiv:1609.01193 [math.CO], 2016.

M. R. Sepanski, On Divisibility of Convolutions of Central Binomial Coefficients, Electronic Journal of Combinatorics, 21 (1) 2014, #P1.32.

Jian Zhou, Fat and Thin Emergent Geometries of Hermitian One-Matrix Models, arXiv:1810.03883 [math-ph], 2018.

FORMULA

G.f. is the series reversion of x-3*x^2+2*x^3.

a(n) = 2^n(3n)!!/((n+1)! n!!). - Maxim Krikun (krikun(AT)iecn.u-nancy.fr), May 25 2007

G.f.: 1/6*sqrt(3)*sin(1/3*arcsin(6*sqrt(3)*x))-1/2*cos(1/3*arcsin(6*sqrt(3)*x)). - Vaclav Kotesovec, Oct 21 2012

Conjecture: n*(n-1)*a(n) +(n-1)*(n-2)*a(n-1) -12*(3*n-5)*(3*n-7)*a(n-2) -12*(3*n-8)*(3*n-10)*a(n-3)=0. - R. J. Mathar, Oct 18 2013

a(n) ~ 2^(n - 3/2) * 3^(3*n/2 - 1) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2017

MAPLE

with(combstruct); ar := {EA = Union(Sequence(EA, card >= 2), Prod(Z, Sequence(EA), Sequence(EA))), C=Union(Z, Prod(Z, Z, Sequence(EA), Sequence(EA), Sequence(Union(Sequence(EA, card>=1), Prod(Z, Sequence(EA), Sequence(EA))))))}; seq(count([EA, ar], size=i), i=1..20);

MATHEMATICA

Rest[CoefficientList[Series[1/6*Sqrt[3]*Sin[1/3*ArcSin[6*Sqrt[3]*x]]-1/2*Cos[1/3*ArcSin[6*Sqrt[3]*x]], {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 21 2012 *)

Rest[CoefficientList[InverseSeries[Series[x - 3*x^2 + 2*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)

PROG

(PARI) a(n)=if(n<1, 0, polcoeff(serreverse(x-3*x^2+2*x^3+x*O(x^n)), n))

CROSSREFS

Cf. A143018.

Sequence in context: A105622 A110903 A206351 * A215931 A271777 A014304

Adjacent sequences:  A085611 A085612 A085613 * A085615 A085616 A085617

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 10 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 09:23 EST 2019. Contains 320161 sequences. (Running on oeis4.)