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A179542 Trajectory of 1 under the morphism 1->(1,2,3), 2->(1,2), 3->(1) related to the heptagon and A006356. 1
1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Given M = the generating matrix for the heptagon shown in A006356:

[1,1,1; 1,1,0; 1,0,0] take powers of M, extracting top row getting:

(1,1,1), (3,2,1), (6,5,3), (14,11,6), where left and right columns (offset) =

A006356, and middle column = A006054. n-th iterate of the sequence is

composed of A006356(n) terms parsed into a frequency of 1's, 2's, and 3's

matching the 3-termed vectors with appropriate sums.

LINKS

Table of n, a(n) for n=0..104.

P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.

Index entries for sequences that are fixed points of mappings

EXAMPLE

Starting with 1, the next two iterates are:

(1, 2, 3) -> (1, 2, 3, 1, 2, 1) -> (1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3).

The 3rd iterate has 14 terms composed of six 1's, five 2's, and three 3's; matching the top row of M^3 = (6, 5, 3), sum = 14 = A006356(3).

MATHEMATICA

NestList[ Flatten[ # /. {1 -> {1, 2, 3}, 2 -> {1, 2}, 3 -> 1}] &, {1}, 5] // Flatten (* Robert G. Wilson v, Jul 23 2010 *)

CROSSREFS

Cf. A006356, A006054

Sequence in context: A047896 A073645 A294180 * A082846 A117373 A132677

Adjacent sequences:  A179539 A179540 A179541 * A179543 A179544 A179545

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 18 2010

EXTENSIONS

More terms from Robert G. Wilson v, Jul 23 2010

STATUS

approved

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Last modified October 23 08:57 EDT 2019. Contains 328345 sequences. (Running on oeis4.)