|
Search: id:A091838
|
|
|
| A091838 |
|
a(n) = number of images of the border correlation function for binary words of length n (cf. link). |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Values for even indices seem mysterious, but does A091838(2n+1) = A002878(n), the bisection of Lucas sequence?
|
|
LINKS
|
T. Harju and D. Nowotka, Border correlation of binary words.
|
|
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.
|
|
CROSSREFS
|
Sequence in context: A003403 A034412 A054352 this_sequence A004696 A018063 A000570
Adjacent sequences: A091835 A091836 A091837 this_sequence A091839 A091840 A091841
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), based on the Harju and Nowotka paper, Mar 10 2004
|
|
EXTENSIONS
|
More terms from Dirk Nowotka (nowotka(AT)utu.fi), May 16 2004
|
|
|
Search completed in 0.002 seconds
|
