OFFSET
0,3
COMMENTS
After a chaotic part, at n = 358 the sequence settles down and becomes quasi-periodic with a 6-loop. For some choices of the initial term a(0) the sequence stays chaotic.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
FORMULA
For k >= 0 :
a(358 + 6*k) = 1062 + 18*k.
a(359 + 6*k) = 1068 + 18*k.
a(360 + 6*k) = 1072 + 18*k.
a(361 + 6*k) = 1076 + 18*k.
a(362 + 6*k) = 1079 + 18*k.
a(363 + 6*k) = -717 - 12*k.
EXAMPLE
For n = 0, a(0) = 1.
For n = 1, a(0) is odd, thus a(1) = 0 - 1 = -1.
For n = 2, a(1) is odd, thus a(2) = 1 - (-1) = 2.
For n = 3, a(2) is even, thus a(3) = floor((3*2 + a(2))/2) = 4.
etc.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = If[OddQ[a[n - 1]], n - 1 - a[n - 1], Floor[(3*n - 3 + a[n - 1])/2]]; Array[a, 100, 0] (* Amiram Eldar, Jan 26 2024 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Ctibor O. Zizka, Jan 25 2024
STATUS
approved