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Search: id:A071153
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| A071153 |
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Lukasiewicz word for each rooted plane tree (interpretation e in Stanley's exercise 19) encoded by A014486 (or A063171), 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. |
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+0
12
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| 0, 1, 20, 11, 300, 201, 210, 120, 111, 4000, 3001, 3010, 2020, 2011, 3100, 2101, 2200, 1300, 1201, 2110, 1210, 1120, 1111, 50000, 40001, 40010, 30020, 30011, 40100, 30101, 30200, 20300, 20201, 30110, 20210, 20120, 20111, 41000, 31001, 31010
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Note: this finite decimal representation works only up to the 6917th term, as the 6918th such word is already (10,0,0,0,0,0,0,0,0,0). The sequence A071154 shows the initial portion of this sequence sorted.
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LINKS
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Index entries for sequences related to Lukasiewicz words
A. Karttunen, Gatomorphisms and other excursions amidst the plane trees & parenthesizations (Includes the complete Scheme program for computing this sequence)
R. P. Stanley, Hipparchus, Plutarch, Schrö der and Hough, Am. Math. Monthly, Vol. 104, No. 4, p. 344, 1997.
R. P. Stanley, Exercises on Catalan and Related Numbers
Index entries for sequences related to parenthesizing
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EXAMPLE
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The 11th term of A063171 is 10110010, corresponding to parenthesization ()(())(), thus its Lukasiewicz word is 3010. The 18th term of A063171 is 11011000, corresponding to parenthesization (()(())), thus its Lukasiewicz word is 1201. I.e. in the latter example there is one list on the top-level, which in turn contains two sublists, of which the first is zero elements long, and the second is a sublist containing one empty sublist (the last zero is omitted).
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CROSSREFS
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For n >= 1, the number of zeros in the term a(n) is given by A057514(n)-1. The first digit of each term is given by A057515. Cf. also A014486, A071152, A071154. Corresponding factorial walk encoding: A071155 (A071157, A071159). a(n) = A079436(n)/10.
Adjacent sequences: A071150 A071151 A071152 this_sequence A071154 A071155 A071156
Sequence in context: A040383 A058282 A071160 this_sequence A073868 A040382 A076119
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KEYWORD
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nonn,fini
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AUTHOR
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Antti Karttunen May 14 2002
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