A240808 a(0)=2, a(1)=1, a(2)=0; thereafter a(n) = a(n-1-a(n-1))+a(n-2-a(n-2)) unless a(n-1) <= n-1 or a(n-2) <= n-2 in which case the sequence terminates.
2, 1, 0, 2, 1, 3, 2, 1, 3, 5, 4, 3, 5, 4, 6, 8, 4, 6, 8, 7, 9, 8, 7, 12, 11, 7, 12, 14, 10, 12, 14, 10, 12, 17, 13, 12, 20, 16, 12, 20, 19, 15, 20, 19, 18, 23, 19, 21, 26, 19, 21, 26, 19, 24, 29, 19, 27, 32, 19, 27, 32, 22, 30, 32, 22, 30, 32, 25, 33, 32, 28, 36, 32, 31, 39, 32, 31, 42, 35, 31, 45, 38, 31, 45, 38, 31, 48, 41, 31, 51, 44, 31, 51, 47, 34
Offset: 0
References
- Higham, Jeff and Tanny, Stephen, A tamely chaotic meta-Fibonacci sequence. Twenty-third Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1993). Congr. Numer. 99 (1994), 67-94. [Contains a detailed analysis of this sequence]
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..20000
- Rémy Sigrist, Colored scatterplot of a(n) for n = 0..20000 (where the color is function of n mod 3)
- Index entries for Hofstadter-type sequences
Crossrefs
Programs
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Haskell
a240808 n = a240808_list !! n a240808_list = 2 : 1 : 0 : zipWith (+) xs (tail xs) where xs = map a240808 $ zipWith (-) [1..] $ tail a240808_list -- Reinhard Zumkeller, Apr 17 2014
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Maple
a:=proc(n) option remember; global k; if n = 0 then 2 elif n = 1 then 1 elif n = 2 then 0 else if (a(n-1) <= n-1) and (a(n-2) <= n-2) then a(n-1-a(n-1))+a(n-2-a(n-2)); else lprint("died with n =",n); return (-1); fi; fi; end; [seq(a(n),n=0..100)]; -
Mathematica
a[n_] := a[n] = Switch[n, 0, 2, 1, 1, 2, 0, _, If[a[n - 1] <= n - 1 && a[n - 2] <= n - 2, a[n - 1 - a[n - 1]] + a[n - 2 - a[n - 2]], Print["died with n =", n]; Return[-1]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2024 *)
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