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Search: id:A080237
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| A080237 |
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Start with 1 and apply the process: k-th run is 1, 2, 3, .., a(k-1)+1. |
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+0
11
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| 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also a triangle collected from the Catalan generating tree, with row n containing A000108(n) terms: 1; 1,2; 1,2,1,2,3; 1,2,1,2,3,1,2,1,2,3,1,2,3,4; and ending with n. Rows converge towards A007001, the "last" row.
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LINKS
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C. Banderier, A. Denise, P. Flajolet, M. Bousquet-Melou et al., Generating Functions for Generating Trees, Discrete Mathematics 246(1-3), March 2002, pp. 29-55.
A. Karttunen, Notes concerning A080237-tree and related sequences.
R. P. Stanley, Catalan addendum. See the interpretation (www, "Vertices of height n-1 of the tree T ...").
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FORMULA
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It seems that sum(k=1, n, a(k))= C*n*log(log(n)) + O(n*log(log(n))) with C=0.6....
a(n) = A007814(A014486(n)) (i.e. number of trailing zeros in A063171(n)).
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EXAMPLE
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Sequence begins: 1,(1,2),(1,2),(1,2,3), ...where runs are between 2 parentheses . 5-th run is (1,2) since a(4)=1 and sequence continues: 1,1,2,1,2,1,2,3,1,2....
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CROSSREFS
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Cf. A000002. Positions of ones: A085223. The first occurrence of each n is at A014138(n). See A085178.
Sequence in context: A134156 A067815 A133780 this_sequence A136109 A105265 A061394
Adjacent sequences: A080234 A080235 A080236 this_sequence A080238 A080239 A080240
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KEYWORD
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nonn,tabf
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 18 2003
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EXTENSIONS
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Additional comments from Antti Karttunen (his-firstname.his-surname(AT)gmail.com), Jun 17 2003.
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