OFFSET
1
COMMENTS
This is column 1 of the array A188294.
Is this A003849 with another 0 in front? - R. J. Mathar, Apr 01 2011
From Michel Dekking, Aug 27 2016: (Start)
Answer: yes. Since [-x] = -[x]-1 for all non-integer x, one has for n > 1:
[r] - [nr] - [(1-n)r] = 1 - [nr] + [(n-1)r] + 1 = 2 - ([nr]-[(n-1)r]) = A003849(n-2). (End)
Also, [ns] - [(n-1)s] where s = (3-sqrt(5))/2, therefore a Sturmian sequence with slope s. Also, a fixed point under the transformation (0 ->001, 1 -> 01). - Richard Blavy, Nov 18 2011; transformation corrected by Nathan Fox, May 03 2014
FORMULA
a(n) = [r] - [n*r] - [r-n*r], where r = (1+sqrt(5))/2.
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 31 2011
EXTENSIONS
Name changed by Clark Kimberling, Aug 24 2019
STATUS
approved