

A260444


Infinite palindromic word (a(1),a(2),a(3),...) with initial word w(1) = (1,0,0) and midword sequence (a(n)); see A260390.


4



1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1


COMMENTS

Below, w* denotes the reversal of a word w, and "sequence" and "word" are interchangeable. 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 a guide to related sequences.


LINKS

Table of n, a(n) for n=1..86.


EXAMPLE

w(1) = 100, the initial word.
w(2) = 1001001 ( = 100+1+001, where + = concatenation)
w(3) = w(2)+0+w(2)*
w(4) = w(3)+1+w(3)*


MATHEMATICA

u[1] = {1, 0, 0}; 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[6] (* A260444 *)


CROSSREFS

Cf. A260390.
Sequence in context: A293449 A269625 A285208 * A289034 A188374 A273511
Adjacent sequences: A260441 A260442 A260443 * A260445 A260446 A260447


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Oct 31 2015


STATUS

approved



