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
KEYWORD
easy,nonn,nice
AUTHOR
Henry Bottomley, Nov 29 2000
EXTENSIONS
Second formula corrected by Charles R Greathouse IV, Jul 28 2011
STATUS
approved