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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^(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

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

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Last modified May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)