

A105584


Fixed point of the morphism 1 > 34, 2 > 32, 3 > 12, 4 > 14, starting from a(0) = 1.


0



1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 1, 4, 3
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OFFSET

0,2


COMMENTS

A triangle space fill substitution: characteristic polynomial:x^42*x^32*x^24*x.
This triangle set was obtained by shifting the Heighway's dragon matrix about: M(Heighways's)={{1, 1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1}, {1, 0, 0, 1}} M(triangle)={{0, 0, 1, 1}, {0, 1, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 1}} This result is a permutation of the rows of the matrix. I have obtained three triangle sets and two Heighway's sets by experiments like these.


LINKS

Table of n, a(n) for n=0..104.
F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.
Index entries for sequences that are fixed points of mappings


MATHEMATICA

Flatten[ Nest[ Flatten[ # /. {1 > {3, 4}, 2 > {3, 2}, 3 > {1, 2}, 4 > {1, 4}} &], {1}, 8]] (* Robert G. Wilson v, May 07 2005 *)


CROSSREFS

Sequence in context: A181982 A070194 A323300 * A072064 A105498 A179289
Adjacent sequences: A105581 A105582 A105583 * A105585 A105586 A105587


KEYWORD

nonn


AUTHOR

Roger L. Bagula, May 03 2005


EXTENSIONS

Edited by Robert G. Wilson v, May 07 2005


STATUS

approved



