

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Values for even indices seem mysterious, but does A091838(2n+1) = A002878(n), the bisection of Lucas sequence?


LINKS

Table of n, a(n) for n=1..38.
Tero Harju, Combinatorics on Words  From N. J. A. Sloane, Aug 02 2012
T. Harju and D. Nowotka, Border correlation of binary words.


FORMULA

a(n) < 2^(n1)
a(n) <= F(n) + F(n2)  m where F(i) is the ith 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
Adjacent sequences: A091835 A091836 A091837 * A091839 A091840 A091841


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



