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Search: id:A007001
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| A007001 |
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Trajectory of 1 under the morphism 1 -> 12, 2 -> 123, 3 -> 1234, etc.
(Formerly M0108)
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+0
13
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| 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, 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, 1, 2, 3, 1, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Records in this sequence occur at positions: 1,2,5,14,42,132,429,1430,... ( which appear to be the Catalan numbers A000108) - (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2005)
The records do occur at Catalan numbers. Of the first C(n) numbers, the number that are equal to k is A033184(n,k), with the one n last. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 29 2009]
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REFERENCES
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S. Lehr, J. Shallit and J. Tromp, On the vector space of the automatic reals, Theoret. Comput. Sci. 163 (1996), no. 1-2, 193-210.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. West, Generating trees and forbidden subsequences, Proc. 6th FPSAC [ Conference on Formal Power Series and Algebraic Combinatorics ] (1994), pp. 441-450 (see p. 443).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..4862 (8 iterations)
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.
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FORMULA
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From n>1 onward a(n) = A080237(A081291(n-1)). - Antti Karttunen (Antti.Karttunen(AT)iki.fi), Jul 31 2003
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MATHEMATICA
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Nest[ Flatten[ # /. a_Integer -> Range[a + 1]] &, {1}, 6] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006)
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PROGRAM
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(PARI) a(n)=local(v, w); if(n<1, 0, v=[1]; while(#v<n, w=[]; for(i=1, #v, w=concat(w, vector(v[i]+1, j, j))); v=w); v[n])
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CROSSREFS
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Cf. A000245, A085182. a(n)=A076050(n)-1. Partial sums: A080336. Positions of ones: A085197. The first occurrence of each n is at A000108(n). See A085180.
Sequence in context: A106394 A091412 A106036 this_sequence A094917 A082691 A036043
Adjacent sequences: A006998 A006999 A007000 this_sequence A007002 A007003 A007004
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Jim Propp (propp(AT)math.wisc.edu)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 22 2000
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