login
A091838
a(n) is the number of images of the border correlation function for binary words of length n (cf. link).
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, 3010349, 4870847, 7881196, 12752041, 20633239, 33385280, 54018521, 87403801
OFFSET
1,2
COMMENTS
Values for even indices seem mysterious, but does A091838(2n+1) = A002878(n), the bisection of Lucas sequence?
LINKS
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: A034412 A289131 A054352 * A288219 A004696 A293418
KEYWORD
nonn
AUTHOR
Benoit Cloitre, based on the Harju and Nowotka paper, Mar 10 2004
EXTENSIONS
More terms from Dirk Nowotka (nowotka(AT)utu.fi), May 16 2004
a(31)-a(38) from Lars Blomberg, Jan 17 2019
STATUS
approved