OFFSET
0,5
LINKS
Peter Kagey, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
FORMULA
a(3k) = k; a(3k + 1) = 3k; a(3k + 2) = 3k + 1.
a(n) = 2*a(n-3) - a(n-6) for n>5. - Colin Barker, Jul 23 2015
G.f.: x^2*(2*x^3+3*x^2+x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, Jul 23 2015
EXAMPLE
a(5) = 5 - 1 = 4 because 5 is not divisible by 3.
a(12) = 12/3 = 4 because 12 is divisible by 3.
MATHEMATICA
Table[If[Mod[n, 3] == 0, n/3, n - 1], {n, 0, 69}] (* or *)
CoefficientList[Series[x^2*(2 x^3 + 3 x^2 + x + 1)/((x - 1)^2*(x^2 + x + 1)^2), {x, 0, 69}], x] (* Michael De Vlieger, Jul 23 2015 *)
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {0, 0, 1, 1, 3, 4}, 80] (* Harvey P. Dale, May 20 2018 *)
PROG
(Ruby) def a(n); (n%3==0)?n/3:n-1 end
(PARI) concat([0, 0], Vec(x^2*(2*x^3+3*x^2+x+1) / ((x-1)^2*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Jul 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Kagey, Jul 22 2015
STATUS
approved