OFFSET
0,2
COMMENTS
Let W(i,j) denote the index of that row of the extended Wythoff array (see A035513) that contains the sequence formed by the sum of rows i and j. Then the "Kim-sum" or "Kimberling-sum" K_n + K_i is W(i-1,n). - N. J. A. Sloane, Mar 08 2016
The n-th Kimberling sequence K_n is defined (cf Links) by K_n(i) = K_n(i-1) + K_n(i-2), with initial values K_n(0) = n, K_n(1) = floor((n+1)*tau). - M. F. Hasler, Sep 02 2016
REFERENCES
J. H. Conway, Posting to Math Fun Mailing List, Dec 02 1996.
M. LeBrun, Posting to Math-Fun Mailing List Jan 10 1997.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..10000
J. H. Conway, Allan Wechsler, Marc LeBrun, Dan Hoey, N. J. A. Sloane, On Kimberling Sums and Para-Fibonacci Sequences, Correspondence and Postings to Math-Fun Mailing List, Nov 1996 to Jan 1997
FORMULA
a(n) = 1 if n=0, otherwise a(n) = A000201(n)+n+3. - N. J. A. Sloane, Mar 07 2016
MATHEMATICA
a[n_] := If[n == 0, 1, Floor[n GoldenRatio] + n + 3];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 15 2023 *)
PROG
(Python)
from math import isqrt
def A022413(n): return (n+isqrt(5*n**2)>>1)+n+3 if n else 1 # Chai Wah Wu, Aug 29 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and extended by N. J. A. Sloane, Mar 07 2016
STATUS
approved