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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 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 October 27 23:01 EDT 2020. Contains 338045 sequences. (Running on oeis4.)