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 A022414 Kim-sums: "Kimberling sums" K_n + K_3. 4
 2, 7, 10, 4, 15, 18, 20, 23, 9, 28, 31, 12, 36, 39, 41, 44, 17, 49, 52, 54, 57, 22, 62, 65, 25, 70, 73, 75, 78, 30, 83, 86, 33, 91, 94, 96, 99, 38, 104, 107, 109, 112, 43, 117, 120, 46, 125, 128, 130, 133, 51, 138, 141, 143, 146, 56, 151, 154, 59, 159, 162, 164, 167 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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 a(n) = W(2,n). - N. J. A. Sloane, Mar 07 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 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 MAPLE Ki := proc(n, i) option remember; local phi ; phi := (1+sqrt(5))/2 ; if i= 0 then n; elif i=1 then floor((n+1)*phi) ; else procname(n, i-1)+procname(n, i-2) ; end if; end proc: Kisum := proc(n, m) local ks, a, i; ks := [seq( Ki(n, i)+Ki(m, i), i=0..5)] ; for i from 0 to 2 do for a from 0 do if Ki(a, 0) = ks[i+1] and Ki(a, 1) = ks[i+2] then return a; end if; if Ki(a, 0) > ks[i+1] then break; end if; end do: end do: end proc: A022414 := proc(n) if n = 0 then 2; else Kisum(n-1, 2) ; end if; end proc: seq(A022414(i), i=0..80) ; # R. J. Mathar, Sep 03 2016 CROSSREFS Cf. A000201, A035513. The "Kim-sums" K_n + K_i for i = 2 through 12 are given in A022413, A022414, A022415, A022416, ..., A022423. Sequence in context: A041453 A042157 A012937 * A319932 A236243 A024831 Adjacent sequences: A022411 A022412 A022413 * A022415 A022416 A022417 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 21 09:44 EDT 2023. Contains 361402 sequences. (Running on oeis4.)