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A006664 Number of irreducible systems of meanders.
(Formerly M1871)
3
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 (list; graph; refs; listen; history; text; internal format)
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: A266507 A202081 A258315 * 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

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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)