The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A189663 Partial sums of A189661. 10
 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS See A189661. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..5000 FORMULA a(n) = 2*(n-1)-floor((n-1)*r), where r = (1+sqrt(5))/2 (the golden ratio). - corrected by R. J. Mathar, Sep 11 2011 a(n) = a(1+a(n-2))+a(n-1-a(n-2)), n>2. - Frank Ruskey, Dec 10 2011 a(1) = 0, a(2) = 1; a(n) = n - a(n-1) - a(n-a(n-1)) for n > 2. - Altug Alkan, Jun 24 2017 a(n) = ceiling((n-1)/r^2), where r = (1+sqrt(5))/2. -Jeffrey Shallit, Jul 02 2018 MATHEMATICA (See A189661.) Table[2 (n - 1) - Floor[(n - 1) (1 + Sqrt) / 2], {n, 100}] (* Vincenzo Librandi, Jun 26 2017 *) PROG (Python) l=[0, 0, 1] for n in range(3, 101): l+=[n - l[n - 1] - l[n - l[n - 1]], ] print l[1:] # Indranil Ghosh, Jun 24 2017, after Altug Alkan (MAGMA) [2*(n-1)-Floor((n-1)*(1+Sqrt(5))/2): n in [1..100]]; // Vincenzo Librandi, Jun 26 2017 CROSSREFS Cf. A001622, A189661, A189662, A026356. Sequence in context: A057367 A032634 A057366 * A061375 A029920 A100719 Adjacent sequences:  A189660 A189661 A189662 * A189664 A189665 A189666 KEYWORD nonn AUTHOR Clark Kimberling, Apr 25 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)