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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
Antti 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.
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 *)
Array[Map[FromDigits[# /. -1->0]*20 &, Select[Permutations[Join[Table[-1, #-1], Table[1, #]]], Min[Accumulate[#]] >=0 &]]&, 6, 0] (* Paolo Xausa, Mar 12 2024 *)
PROG
(Python)
from itertools import count, islice
from sympy.utilities.iterables import multiset_permutations
def A071152_gen(): # generator of terms
yield 0
for l in count(1):
for s in multiset_permutations('0'*l+'1'*(l-1)):
c, m = 0, (l<<1)-1
for i in range(m):
if s[i] == '1':
c += 2
if c<i:
break
else:
yield 10**m+int(''.join(s))<<1
A071152_list = list(islice(A071152_gen(), 30)) # Chai Wah Wu, Nov 28 2023
CROSSREFS
a(n) = 2*A063171(n) = A071153(A057123(n)).
Sequence in context: A267575 A072818 A123479 * A195622 A305658 A329067
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 14 2002
STATUS
approved

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Last modified April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)