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A260445 Infinite palindromic word (a(1),a(2),a(3),...) with initial word w(1) = (0,0,1) and midword sequence (a(n)); see Comments. 3
0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 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 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

FORMULA

Formula:  a(n) = 1 - A260397(n).

EXAMPLE

w(1) = 001, the initial word.

w(2) = 0010100 ( = 001+0+100, where + = concatenation)

w(3) = w(2)+1+w(2)*

w(4) = w(3)+0+w(3)*

MATHEMATICA

u[1] = { 0, 0, 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]]}; u[6]

CROSSREFS

Cf. A260390, A260397.

Sequence in context: A059125 A189820 A111406 * A156731 A254379 A288257

Adjacent sequences:  A260442 A260443 A260444 * A260446 A260447 A260448

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 22 2015

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)