0,2

Many authors use the term "unbordered" for "bifix-free". The Lothaire (1997) reference refers to bifix-free words as primary words (Chapter 8). - David Callan (callan(AT)stat.wisc.edu), Sep 25 2006

G. Blom, Problem 94-20: Overlapping binary sequences, SIAM Review 37 (1995), 619-620.

L. J. Guibas and A. M. Odlyzko; Periods in Strings, Journal of Combinatorial Theory A 30 (1981) 19-42. Their L_n(0) is A003000[n].

H. Harborth, Endliche 0-1-Folgen mit gleichen Teilbl\"ocken, J. f\"ur Reine Angewandte Math. 271 (1974), 139-154, see p. 143.

P. Tolstrup Nielsen, A note on bifix-free sequences, IEEE Trans. Info. Theory IT-19 (1973), 704-706.

M. Lothaire, Combinatorics on Words, Cambridge University Press, NY, 1997.

D. J. Greaves and S. J. Montgomery-Smith, Unforgeable Marker Sequences.

T. Harju and D. Nowotka, Border correlation of binary words.

Guy P. Srinivasan, Java program for this sequence and A122536

a(2n+1) = 2a(2n), a(2n) = 2a(2n-1) - a(n).

A003000[n]/2^n converges to 0.2677868402178891123766714035843025525550598979934845320763118885112149...

a(0)=1; a(n)=2*a(n-1)-1/2*(1+(-1)^n)*a([n/2]). - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jun 10 2004

a[0]=1; a[n_]:=a[n]=2*a[n-1]-(1+(-1)^n)/2*a[Floor[n/2]]; Table[a[n], {n, 0, 34}]

a[0]=1; a[n_]:=a[n]=2*a[n-1]-If[EvenQ[n], a[n/2], 0] (Ed Pegg, Jr., (ed(AT)mathpuzzle.com), Jan 05 2005)

Equals 2 * A045690 for n > 0. Complement gives A094536. Cf. A019308, A019309, A094536, A094537.

Cf. A094536, A094537.

Adjacent sequences: A002997 A002998 A002999 this_sequence A003001 A003002 A003003

Sequence in context: A001679 A030435 A063886 this_sequence A122536 A128209 A052953

nonn,easy,nice

njas

New description and reference from Jeffrey Shallit Sep 15 1996. Additional comments from TORSTEN.SILLKE(AT)LHSYSTEMS.COM, Jan 17, 2001.

More terms from Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jun 10 2004