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A306314 Number of length-n binary words w such that ww is rich. 0
2, 4, 8, 16, 32, 52, 100, 160, 260, 424, 684, 988, 1588, 2342, 3458, 5072, 7516, 10546, 15506, 21496, 30682, 42508, 60170, 81316, 114182, 153768, 212966, 283502, 390168, 513652 (list; graph; refs; listen; history; text; internal format)



A rich word w is one that contains, as contiguous subwords, exactly n nonempty palindromes, where n is the length of w.  An infinite word is rich if all of its (contiguous) subwords are rich.  By a theorem of Glen, Justin, Widmer, and Zamboni (below), a(n) is also the number of length-n binary words w such that the infinite word www... is rich.  And also the number of length-n binary words w that are products of two palindromes, where all the conjugates of w are rich.


Table of n, a(n) for n=1..30.

A. Glen, J. Justin, S. Widmer, and L. Q. Zamboni, Palindromicrichness, European J. Combinatorics 30 (2009), 510-531.  See Theorem 3.1, p. 515


Cf. A216264.

Sequence in context: A226930 A326751 A297702 * A007055 A175951 A072207

Adjacent sequences:  A306311 A306312 A306313 * A306315 A306316 A306317




Jeffrey Shallit, Feb 06 2019


a(17)-a(30) from Lars Blomberg, Feb 13 2019



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Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)