A179542 Trajectory of 1 under the morphism 1->(1,2,3), 2->(1,2), 3->(1) related to the heptagon and A006356.

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

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