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A058207
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Three steps forward, two steps back.
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2
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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; internal format)
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OFFSET
| 0,3
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
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FORMULA
| 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^2)(1+x)^2+x^3)/(1-x^5)^2.
a(n)=n/5+4/5*((n mod 5)mod 4)+6/5*floor((n mod 5)/4) [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Jul 26 2009]
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MATHEMATICA
| a[n_] := Quotient[n, 5] + {0, 1, 2, 3, 2}[[Mod[n, 5] + 1]]; Table[a[n], {n, 0, 82}] (* From Jean-François Alcover, Dec 12 2011, after Charles R Greathouse IV *)
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PROG
| (MAGMA) [ n le 4 select n-1 else n eq 5 select 2 else Self(n-5)+1: n in [1..83] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 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)
-- Reinhard Zumkeller, Jul 28 2011
(PARI) a(n)=n\5+[0, 1, 2, 3, 2][n%5+1] \\ Charles R Greathouse IV, Jul 28 2011
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CROSSREFS
| Cf. A008611.
Sequence in context: A152978 A118121 A006968 * A105969 A163530 A114409
Adjacent sequences: A058204 A058205 A058206 * A058208 A058209 A058210
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 29 2000
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EXTENSIONS
| Formula corrected by Charles R Greathouse IV, Jul 28 2011
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