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A022413
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Kim-sums: "Kimberling sums" K_n + K_2.
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6
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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
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graph;
refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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J. H. Conway, Posting to Math Fun Mailing List, Dec 02 1996.
M. LeBrun, Posting to Math-Fun Mailing List Jan 10 1997.
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LINKS
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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
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FORMULA
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a(n) = 1 if n=0, otherwise a(n) = A000201(n)+n+3. - N. J. A. Sloane, Mar 07 2016
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PROG
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(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
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CROSSREFS
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Cf. A000201, A035513.
The "Kim-sums" K_n + K_i for i = 2 through 12 are given in A022413, A022414, A022415, ..., A022423.
Sequence in context: A335495 A355569 A280537 * A078781 A256359 A287073
Adjacent sequences: A022410 A022411 A022412 * A022414 A022415 A022416
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KEYWORD
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nonn
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AUTHOR
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Marc LeBrun
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EXTENSIONS
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Edited and extended by N. J. A. Sloane, Mar 07 2016
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STATUS
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approved
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