

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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..24.
A. Karttunen, Collection of sourcecode 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 standalone 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] (* JeanFrançois 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



