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A330127
Number of length-n binary words containing at most distinct 11 palindromes as subwords (including the empty word).
0
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 292, 270, 268, 276, 276, 288, 320, 340, 364, 388, 404, 428, 476, 512, 560, 610, 644, 692, 768, 840, 924, 1020, 1100, 1190, 1316, 1452, 1612, 1786, 1952, 2134, 2348, 2598, 2896, 3228, 3552, 3908, 4300, 4752, 5296
OFFSET
0,2
COMMENTS
Asymptotically, a(n) ~ c*alpha^n, where alpha ~ 1.1127756842787054706297 is the largest positive real zero of X^7 - X - 1 and c ~ 20.665.
LINKS
Gabriele Fici and Luca Q. Zamboni, On the least number of palindromes contained in an infinite word, Theor. Comput. Sci. 481 (2013), 1-8.
Lukas Fleischer, Jeffrey Shallit, Words With Few Palindromes, Revisited, arxiv preprint arXiv:1911.12464 [cs.FL], November 27 2019.
FORMULA
a(n) = -a(n - 1) - a(n - 2) - a(n - 3) - a(n - 4) - a(n - 5) + 2a(n - 6) + 4a(n - 7) + 5a(n - 8) + 5a(n - 9) + 5a(n - 10) + 5a(n - 11) + 2a(n - 12) - 3a(n - 13) + -6a(n - 14) - 8a(n - 15) - 8a(n - 16) - 8a(n - 17) - 7a(n - 18) - 3a(n - 19) + 3a(n - 21) + 4a(n - 22) + 4a(n - 23) + 4a(n - 24) + 3a(n - 25) + 2a(n - 26) + a(n - 27) for n >= 42.
CROSSREFS
Sequence in context: A113699 A113010 A366855 * A292568 A354600 A056767
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Dec 02 2019
STATUS
approved