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A058207
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Three steps forward, two steps back.
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9
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0, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 7, 6, 7, 8, 9, 8, 7, 8, 9, 10, 9, 8, 9, 10, 11, 10, 9, 10, 11, 12, 11, 10, 11, 12, 13, 12, 11, 12, 13, 14, 13, 12, 13, 14, 15, 14, 13, 14, 15, 16, 15, 14, 15, 16, 17, 16, 15, 16, 17, 18, 17, 16, 17, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = a(n-5) + 1.
a(n) = a(n-1) + 1 if n=1, 2 or 3 mod 5.
a(n) = a(n-1) - 1 if n=0 or 4 mod 5.
G.f.: (x*(1+x+x^2-x^3-x^4))/((x-1)^2*(1+x+x^2+x^3+x^4)). [Corrected by Georg Fischer, May 18 2019]
a(n) = n/5 + 4/5*((n mod 5) mod 4) + (6/5)*floor((n mod 5)/4). - Rolf Pleisch, Jul 26 2009
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MAPLE
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MATHEMATICA
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a[n_] := Quotient[n, 5] + {0, 1, 2, 3, 2}[[Mod[n, 5] + 1]]; Table[a[n], {n, 0, 82}] (* Jean-François Alcover, Dec 12 2011, after Charles R Greathouse IV *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 2, 1}, 110] (* Harvey P. Dale, Feb 27 2013 *)
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PROG
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(Magma) [ n le 4 select n-1 else n eq 5 select 2 else Self(n-5)+1: n in [1..83] ]; // Klaus Brockhaus, Apr 14 2009
(Haskell)
a058207 n = a058207_list !! n
a058207_list = f [0, 1, 2, 3, 2] where f xs = xs ++ f (map (+ 1) xs)
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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