|
|
A022413
|
|
Kim-sums: "Kimberling sums" K_n + K_2.
|
|
6
|
|
|
1, 5, 8, 10, 13, 16, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 44, 47, 50, 52, 55, 57, 60, 63, 65, 68, 71, 73, 76, 78, 81, 84, 86, 89, 92, 94, 97, 99, 102, 105, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, 133, 136, 139, 141, 144, 146, 149, 152, 154, 157, 160, 162, 165, 167, 170, 173, 175, 178
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
a[n_] := If[n == 0, 1, Floor[n GoldenRatio] + n + 3];
|
|
PROG
|
(Python)
from math import isqrt
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|