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A003160
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a(1) = a(2) = 1, a(n) = n - a(a(n-1)) - a(a(n-2)).
(Formerly M0446)
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7
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1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 34, 35, 36, 36, 36, 37, 37, 37, 38
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OFFSET
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1,4
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COMMENTS
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Sequence of indices n where a(n-1) < a(n) appears to be given by A003156. - Joerg Arndt, May 11 2010
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) is asymptotic to n/2.
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MATHEMATICA
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Block[{a = {1, 1}}, Do[AppendTo[a, i - a[[ a[[-1]] ]] - a[[ a[[-2]] ]] ], {i, 3, 76}]; a] (* Michael De Vlieger, Dec 31 2020 *)
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PROG
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(PARI) a(n)=if(n<3, 1, n-a(a(n-1))-a(a(n-2)))
(Haskell)
a003160 n = a003160_list !! (n-1)
a003160_list = 1 : 1 : zipWith (-) [3..] (zipWith (+) xs $ tail xs)
where xs = map a003160 a003160_list
(SageMath)
@CachedFunction
def a(n): return 1 if (n<3) else n - a(a(n-1)) - a(a(n-2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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