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 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 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

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Last modified December 9 17:08 EST 2018. Contains 318023 sequences. (Running on oeis4.)