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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292460 Expansion of (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3) in powers of x. 3
1, 1, 2, 4, 8, 17, 37, 82, 185, 423, 978, 2283, 5373, 12735, 30372, 72832, 175502, 424748, 1032004, 2516347, 6155441, 15101701, 37150472, 91618049, 226460893, 560954047, 1392251012, 3461824644, 8622571758, 21511212261, 53745962199, 134474581374 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of U_{k}D-equivalence classes of Łukasiewicz paths. Łukasiewicz paths are P-equivalent iff the positions of pattern P are identical in these paths. - Sergey Kirgizov, Apr 08 2018

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Jean-Luc Baril, Sergey Kirgizov and Armen Petrossian, Enumeration of Łukasiewicz paths modulo some patterns, arXiv:1804.01293 [math.CO], 2018.

FORMULA

G.f.: 1/(1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(... (continued fraction).

a(n) = A004148(n+1).

a(n) ~ 5^(1/4) * phi^(2*n + 4) / (2*sqrt(Pi)*n^(3/2)), where phi is the golden ratio (1+sqrt(5))/2. - Vaclav Kotesovec, Sep 17 2017

MATHEMATICA

CoefficientList[Series[(1-x-x^2 -Sqrt[(1-x-x^2)^2 -4*x^3])/(2*x^3), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2018 *)

PROG

(PARI) x='x+O('x^50); Vec((1-x-x^2 -sqrt((1-x-x^2)^2 -4*x^3))/(2*x^3)) \\ G. C. Greubel, Aug 13 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2 -Sqrt((1-x-x^2)^2 -4*x^3))/(2*x^3))); // G. C. Greubel, Aug 13 2018

CROSSREFS

Cf. A001006, A004148, A292461.

Sequence in context: A292461 A203019 A004148 * A085022 A003426 A179476

Adjacent sequences:  A292457 A292458 A292459 * A292461 A292462 A292463

KEYWORD

nonn,changed

AUTHOR

Seiichi Manyama, Sep 16 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 01:39 EDT 2018. Contains 313840 sequences. (Running on oeis4.)