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A007001 Trajectory of 1 under the morphism 1 -> 12, 2 -> 123, 3 -> 1234, etc.
(Formerly M0108)
15
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Records in this sequence occur at positions: 1, 2, 5, 14, 42, 132, 429, 1430, ... (which appear to be the Catalan numbers A000108). - Robert G. Wilson v, 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. - Franklin T. Adams-Watters, Mar 29 2009

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n=1..4862 (8 iterations)

C. Banderier, A. Denise, P. Flajolet, M. Bousquet-Mélou 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.

James Propp and N. J. A. Sloane, Email, March 1994

Index entries for sequences that are fixed points of mappings

FORMULA

From n>1 onward a(n) = A080237(A081291(n-1)). - Antti Karttunen, Jul 31 2003

MATHEMATICA

Nest[ Flatten[ # /. a_Integer -> Range[a + 1]] &, {1}, 6] (* Robert G. Wilson v, Jan 24 2006 *)

PROG

(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])

CROSSREFS

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: A171712 A091412 A106036 * A094917 A082691 A280052

Adjacent sequences:  A006998 A006999 A007000 * A007002 A007003 A007004

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein, James Propp

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Sep 22 2000

STATUS

approved

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Last modified December 17 00:23 EST 2017. Contains 296096 sequences.