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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.

%I A071152 #58 Mar 12 2024 19:01:36
%S A071152 0,20,2020,2200,202020,202200,220020,220200,222000,20202020,20202200,
%T A071152 20220020,20220200,20222000,22002020,22002200,22020020,22020200,
%U A071152 22022000,22200020,22200200,22202000,22220000,2020202020,2020202200
%N 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.
%H A071152 Paolo Xausa, <a href="/A071152/b071152.txt">Table of n, a(n) for n = 0..23713</a>
%H A071152 Indranil Ghosh, <a href="/A071152/a071152.txt">Python program for computing this sequence</a>
%H A071152 Antti Karttunen, <a href="https://web.archive.org/web/20070114104000/http://ndirty.cute.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Collection of source-code for this and similar sequences in Internet Archive</a> (Look especially in the first three modules, gatomain.scm, gatorank.scm and gatoaltr.scm. To be replaced later with a stand-alone code.)
%H A071152 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/papers/hip.pdf">Hipparchus, Plutarch, Schröder and Hough</a>, Am. Math. Monthly, Vol. 104, No. 4, p. 344, 1997.
%H A071152 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a>
%H A071152 OEIS Wiki, <a href="/wiki/Łukasiewicz_words">Łukasiewicz words</a>
%H A071152 <a href="/index/Lu#Lukasiewicz">Index entries for sequences related to Łukasiewicz</a>
%F A071152 a(n) = 2*A063171(n).
%t A071152 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 *)
%t A071152 Array[Map[FromDigits[# /. -1->0]*20 &, Select[Permutations[Join[Table[-1, #-1], Table[1,#]]], Min[Accumulate[#]] >=0 &]]&, 6, 0] (* _Paolo Xausa_, Mar 12 2024 *)
%o A071152 (Python)
%o A071152 from itertools import count, islice
%o A071152 from sympy.utilities.iterables import multiset_permutations
%o A071152 def A071152_gen(): # generator of terms
%o A071152     yield 0
%o A071152     for l in count(1):
%o A071152         for s in multiset_permutations('0'*l+'1'*(l-1)):
%o A071152             c, m = 0, (l<<1)-1
%o A071152             for i in range(m):
%o A071152                 if s[i] == '1':
%o A071152                     c += 2
%o A071152                 if c<i:
%o A071152                     break
%o A071152             else:
%o A071152                 yield 10**m+int(''.join(s))<<1
%o A071152 A071152_list = list(islice(A071152_gen(),30)) # _Chai Wah Wu_, Nov 28 2023
%Y A071152 a(n) = 2*A063171(n) = A071153(A057123(n)).
%Y A071152 Cf. A014486, A059984, A059985, A071153, A071154, A079436.
%K A071152 nonn
%O A071152 0,2
%A A071152 _Antti Karttunen_, May 14 2002