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A058207 Three steps forward, two steps back. 9
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)
OFFSET

0,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

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). - Rolf Pleisch, Jul 26 2009

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/5). - Wesley Ivan Hurt, Oct 28 2015

MAPLE

A058207:=n->add((-1)^floor((2*i-2)/5), i=1..n): seq(A058207(n), n=0..100); # Wesley Ivan Hurt, Oct 28 2015

MATHEMATICA

a[n_] := Quotient[n, 5] + {0, 1, 2, 3, 2}[[Mod[n, 5] + 1]]; Table[a[n], {n, 0, 82}] (* Jean-Fran├žois 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 *)

PROG

(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)

-- 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

CROSSREFS

Cf. A008611.

Sequence in context: A152978 A118121 A006968 * A105969 A275892 A163530

Adjacent sequences:  A058204 A058205 A058206 * A058208 A058209 A058210

KEYWORD

easy,nonn,nice

AUTHOR

Henry Bottomley, Nov 29 2000

EXTENSIONS

Second formula corrected by Charles R Greathouse IV, Jul 28 2011

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)