OFFSET
0,1
COMMENTS
Decimal expansion of 1/3. - Raymond Wang, Mar 06 2010
Continued fraction expansion of (3+sqrt(13))/2. - Bruno Berselli, Mar 15 2011
LINKS
Tanya Khovanova, Recursive Sequences.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1011.
Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seqs., Vol. 6 (2003), Article 03.1.6.
Rick Mabry, Proof without words: 1/4+(1/4)^2+(1/4)^3+...=1/3, Math. Mag., Vol. 72, No. 1 (1999), p. 63.
Index entries for linear recurrences with constant coefficients, signature (1).
FORMULA
G.f.: 3/(1-x). - Bruno Berselli, Mar 15 2011
E.g.f.: 3*e^x. - Vincenzo Librandi, Jan 24 2012
a(n) = 3*A000012(n). - Michel Marcus, Dec 18 2015
a(n) = floor(1/(n - cot(1/n))). - Clark Kimberling, Mar 10 2020
Equals Sum_{k>=1} (1/4)^k (as a constant). - Michel Marcus, Jun 11 2020
Equals Sum_{k>=2} (k-1)/binomial(2*k,k) (as a constant). - Amiram Eldar, Jun 05 2021
Equals Sum_{k>=1} (-1)^(k+1)/2^k. - Michal Paulovic, Mar 02 2023
EXAMPLE
1/3 = 0.33333333333333333333333333333333333333333333... - Bruno Berselli, Mar 21 2014
MAPLE
evalf(1/3, 100); # Michal Paulovic, Mar 02 2023
MATHEMATICA
Table[3, {100}] (* Wesley Ivan Hurt, Jul 16 2014 *)
PROG
(Haskell)
a010701 = const 3
a010701_list = repeat 3 -- Reinhard Zumkeller, May 07 2012
(Maxima) makelist(3, n, 0, 30); /* Martin Ettl, Nov 09 2012 */
(PARI) a(n)=3 \\ Felix Fröhlich, Jul 16 2014
(Python)
def A010701(n): return 3 # Chai Wah Wu, Nov 10 2022
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved