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

Author

Henry Bottomley, Nov 29 2000

Keywords

• easy
• nonn
• nice

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).

Crossrefs

Cf. A008611.

Programs

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

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

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 *)

PARI

a(n)=n\5+[0,1,2,3,2][n%5+1] \\ Charles R Greathouse IV, Jul 28 2011

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

Extensions

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