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A071152 Łukasiewicz words for the rooted plane binary trees (interpretation d in Stanley's exercise 19) with the last leaf implicit, i.e., these words are given without the last trailing zero, except for the null tree which is encoded as 0. 3
0, 20, 2020, 2200, 202020, 202200, 220020, 220200, 222000, 20202020, 20202200, 20220020, 20220200, 20222000, 22002020, 22002200, 22020020, 22020200, 22022000, 22200020, 22200200, 22202000, 22220000, 2020202020, 2020202200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

A. Karttunen, Collection of source-code for this and similar sequences in Internet Archive (Look especially in the first three modules, gatomain.scm, gatorank.scm and gatoaltr.scm. To be replaced later with a stand-alone code.)

R. P. Stanley, Hipparchus, Plutarch, Schröder and Hough, Am. Math. Monthly, Vol. 104, No. 4, p. 344, 1997.

R. P. Stanley, Exercises on Catalan and Related Numbers

OEIS Wiki, Łukasiewicz words

Indranil Ghosh, Python program for computing this sequence

Index entries for sequences related to Łukasiewicz

FORMULA

a(n) = 2*A063171(n).

MATHEMATICA

balancedQ[0] = True; balancedQ[n_] := (s = 0; Do[s += If[b == 1, 1, -1]; If[s < 0, Return[False]], {b, IntegerDigits[n, 2]}]; Return[s == 0]); 2*FromDigits /@ IntegerDigits[ Select[Range[0, 684], balancedQ], 2] (* Jean-François Alcover, Jul 24 2013 *)

CROSSREFS

a(n) = 2*A063171(n) = A071153(A057123(n)).

Cf. A014486, A059984, A059985, A071153, A071154, A079436.

Sequence in context: A267575 A072818 A123479 * A195622 A305658 A064878

Adjacent sequences:  A071149 A071150 A071151 * A071153 A071154 A071155

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 14 2002

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)