OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(2*k-1) = k, a(4*k) = 2*k-1, a(4*k-2) = 2*k, for k >= 1.
From Colin Barker, Apr 08 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.
G.f.: x*(1+x-x^3+x^4) / ((1-x)^2*(1+x)*(1+x^2)). (End)
a(n) = (2*n+1-4*cos(n*Pi/2)-cos(n*Pi))/4. - Wesley Ivan Hurt, Oct 02 2017
EXAMPLE
The fifth run of successive numbers in A068225 is 8, 9, 10 with run length three so a(5) = 3.
MATHEMATICA
Rest@ CoefficientList[Series[x (1 + x - x^3 + x^4)/((1 - x)^2*(1 + x) (1 + x^2)), {x, 0, 75}], x] (* Michael De Vlieger, Oct 02 2017 *)
PROG
(PARI) a(n) = if(n%2==1, (n+1)/2, if(n%4==0, (n/2)-1, (n/2)+1))
for(n=1, 80, print1(a(n), ", "))
(PARI) Vec(x*(1+x-x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100)) \\ Colin Barker, Apr 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rick L. Shepherd, Aug 03 2006
STATUS
approved