A058207 Three steps forward, two steps back.

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

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+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

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-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 *)

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