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A091838
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a(n) = number of images of the border correlation function for binary words of length n (cf. link).
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1
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1, 2, 4, 7, 11, 18, 29, 47, 76, 121, 199, 310, 521, 841, 1364, 2207, 3571, 5776, 9349, 15125, 24476, 39601, 64079, 103682, 167761, 271441, 439204, 710645, 1149851, 1860496
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Values for even indices seem mysterious, but does A091838(2n+1) = A002878(n), the bisection of Lucas sequence?
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LINKS
| T. Harju and D. Nowotka, Border correlation of binary words.
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FORMULA
| a(n) < 2^(n-1)
a(n) <= F(n) + F(n-2) - m where F(i) is the i-th Fibonacci number and m=2 if n is in the set {2i | i >= 0} - {2^j, 3x2^j | j >= 0} - Dirk Nowotka (nowotka(AT)utu.fi), May 16 2004
a(n) seems to be asymptotic to phi^n where phi=(1+sqrt(5))/2.
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CROSSREFS
| Sequence in context: A003403 A034412 A054352 * A004696 A018063 A000570
Adjacent sequences: A091835 A091836 A091837 * A091839 A091840 A091841
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), based on the Harju and Nowotka paper, Mar 10 2004
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EXTENSIONS
| More terms from Dirk Nowotka (nowotka(AT)utu.fi), May 16 2004
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