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 A022416 Kim-sums: "Kimberling sums" K_n + K_5. 4
 4, 13, 16, 18, 21, 24, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 79, 81, 84, 86, 89, 92, 94, 97, 100, 102, 105, 107, 110, 113, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 141, 144, 147, 149, 152, 154, 157, 160, 162, 165, 168, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Posting to math-fun mailing list Jan 10 1997. LINKS Table of n, a(n) for n=0..61. 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: A022416 := proc(n) if n = 0 then 4; else Kisum(n-1, 4) ; end if; end proc: seq(A022416(n), n=0..80) ; # R. J. Mathar, Sep 03 2016 MATHEMATICA Ki[n_, i_] := Ki[n, i] = Which[i == 0, n, i == 1, Floor[(n+1)* GoldenRatio], True, Ki[n, i-1] + Ki[n, i-2]]; Kisum[n_, m_] := Module[{ks, a, i}, ks = Table[Ki[n, i] + Ki[m, i], {i, 0, 5}]; For[i = 0, i <= 2, i++, For[a = 0, True, a++, If[Ki[a, 0] == ks[[i+1]] && Ki[a, 1] == ks[[i+2]], Return[a]]; If[Ki[a, 0] > ks[[i+1]], Break[]]]]]; A022416[n_] := If[n == 0, 4, Kisum[n-1, 4]]; Table[A022416[n], {n, 0, 80}] (* Jean-François Alcover, Jun 09 2023, after R. J. Mathar *) CROSSREFS Sequence in context: A126908 A106681 A144947 * A027757 A287361 A165336 Adjacent sequences: A022413 A022414 A022415 * A022417 A022418 A022419 KEYWORD nonn AUTHOR Marc LeBrun STATUS approved

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Last modified August 12 06:37 EDT 2024. Contains 375085 sequences. (Running on oeis4.)