

A260454


Infinite palindromic word (a(1),a(2),a(3),...) with initial word w(1) = (3,2,1) and midword sequence (a(n)); see Comments.


2



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

1,1


COMMENTS

Below, w* denotes the reversal of a word w, and "sequence" and "word" are interchangable. An infinite word is palindromic if it has infinitely many initial subwords w such that w = w*.
Many infinite palindromic words (a(1),a(2),...) are determined by an initial word w and a midword sequence (m(1),m(2),...) of palindromes, as follows: for given w of length k, take w(1) = w = (a(1),a(2),...,a(k)). Form the palindrome w(2) = w(1)m(1)w(1)* by concatenating w(1), m(1), and w(1)*. Continue inductively; i.e., w(n+1) = w(n)m(n)w(n)* for all n >= 1. See A260390 for examples.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

w(1) = 321, the initial word.
w(2) = 3213123 ( = 321+3+123, where + = concatenation)
w(3) = w(2)+2+w(2)*
w(4) = w(3)+1+w(3)*


MATHEMATICA

u[1] = {3, 2, 1}; m[1] = {u[1][[1]]};
u[n_] := u[n] = Join[u[n  1], m[n  1], Reverse[u[n  1]]]
m[k_] := {u[k][[k]]}; v = u[8]


CROSSREFS

Cf. A260390, A260453.
Sequence in context: A112745 A205564 A036585 * A164848 A213514 A130827
Adjacent sequences: A260451 A260452 A260453 * A260455 A260456 A260457


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Aug 29 2015


STATUS

approved



