OFFSET
0,7
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Martin Griffiths, A formula for an infinite family of Fibonacci-word sequences, Fib. Q., 56 (2018), 75-80.
D. R. Hofstadter, Eta-Lore [With permission]
D. R. Hofstadter, Pi-Mu Sequences [With permission]
D. R. Hofstadter and N. J. A. Sloane, Correspondence, 1977 and 1991 (On page 4 of DRH letter, v[n] = A006336, a[n] = A060144[n+1]). - N. J. A. Sloane, Oct 25 2014
FORMULA
For n>0, a(n)=n reduced modulo A005206(n). - Benoit Cloitre, Jan 01 2003
Let n' = n-1. Above formula is better as a(n') = n'-A005206(n'). Also a(n') = A005206(A005206(n'-1)). Also a(n'+1) = n'-a(n')-a(n'-a(n')), with a(0) = 0. - Frank Ruskey, Dec 09 2011
a(n+1) = n - A005206(n). - Reinhard Zumkeller, Apr 07 2012
a(n) = floor(n*A132338). - R. J. Mathar, Jul 29 2021
MAPLE
A060144 := proc(n)
(3+sqrt(5))/2 ;
floor(n/%) ;
end proc:
seq(A060144(n), n=0..100) ; # R. J. Mathar, Jul 29 2021
MATHEMATICA
Table[Floor[n/GoldenRatio^2], {n, 0, 100}] (* T. D. Noe, Dec 10 2011 *)
PROG
(PARI)
{ default(realprecision, 10); f=2/(sqrt(5) + 3); for (n=0, 1000, write("b060144.txt", n, " ", floor(n*f)); ) } \\ Harry J. Smith, Jul 02 2009
(Haskell)
a060144 n = a060144_list !! n
a060144_list = 0 : 0 : scanl1 (+) a003849_list
-- Reinhard Zumkeller, Apr 07 2012
(Python)
from math import isqrt
def A060144(n): return (n<<1)-1-(n+isqrt(5*n**2)>>1) if n else 0 # Chai Wah Wu, Aug 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 05 2001
STATUS
approved