A006664 Number of irreducible systems of meanders. (Formerly M1871)

1, 1, 2, 8, 46, 322, 2546, 21870, 199494, 1904624, 18846714, 191955370, 2002141126, 21303422480, 230553207346, 2531848587534, 28159614749270, 316713536035464, 3597509926531778, 41225699113145888, 476180721050626814, 5539597373695447322, 64863295574835126394, 763984568163192551672, 9047263176444565467566

Offset

0,3

References

V. I. Arnol'd, A branched covering of CP^2->S^4, hyperbolicity and projective topology [ Russian ], Sibir. Mat. Zhurn., 29 (No. 2, 1988), 36-47 = Siberian Math. J., 29 (1988), 717-725.

S. K. Lando and A. K. Zvonkin, "Plane and projective meanders", Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303.

S. K. Lando and A. K. Zvonkin, "Meanders", Selecta Mathematica Sovietica Vol. 11, Number 2, pp. 117-144, 1992.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..24.

Motohisa Fukuda, Ion Nechita, Enumerating meandric systems with large number of components, arXiv preprint arXiv:1609.02756 [math.CO], 2016.

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Séries Formelles et Combinatoire Algébrique. Laboratoire Bordelais de Recherche Informatique, Université Bordeaux I, 1991, pp. 287-303. (Annotated scanned copy)

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.

Formula

A(x^2) = S(x^2)#inv(x*S(x^2)) where # is functional composition, S(x) is g.f. of A001246 (squares of Catalan numbers) and inv(.) is functional inverse. A(x) consists of even-numbered terms of A(x^2), odd terms of which are 0. - Doug McIlroy (doug(AT)cs.dartmouth.edu), Mar 22 2006

Mathematica

terms = 25;
S[x_] = Sum[CatalanNumber[k]^2 x^k, {k, 0, 2 terms}];
inv = InverseSeries[x S[x^2] + O[x]^(2 terms), x] // Normal;
(S[x^2] /. x -> inv) + O[x]^(2 terms) // CoefficientList[#, x]& // DeleteCases[#, 0]& (* Jean-François Alcover, Sep 04 2018 *)

Crossrefs

Sequence in context: A202081 A258315 A334498 * A276367 A326351 A276358

Adjacent sequences: A006661 A006662 A006663 * A006665 A006666 A006667

Keyword

nonn,nice

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Doug McIlroy (doug(AT)cs.dartmouth.edu), Mar 22 2006

Status

approved