A119558 a(1)=0,a(2)=0,a(3)=1 then a(n)=abs(a(n-1)-a(n-2))+(-1)^n*a(n-3).

0, 0, 1, 1, 0, 2, 1, 1, -2, 4, 5, -1, 2, 8, 7, 3, -4, 14, 15, -3, 4, 22, 21, 5, -6, 32, 33, -5, 6, 44, 43, 7, -8, 58, 59, -7, 8, 74, 73, 9, -10, 92, 93, -9, 10, 112, 111, 11, -12, 134, 135, -11, 12, 158, 157, 13, -14, 184, 185, -13, 14, 212, 211, 15, -16, 242, 243, -15, 16, 274, 273, 17, -18, 308, 309, -17, 18, 344

Offset

0,6

Comments

See A104156 for an order 2 example.

References

Benoit Cloitre, On strange predictible recursions, preprint 2006.

Links

Table of n, a(n) for n=0..77.

Formula

for n>=1 a(4n)=(-1)^n*(2*floor(n/2)-1), a(4*n+1)=(-1)^(n+1)*2*floor(n/2), a(4*n+2)=n^2-n+2, a(4*n+3)=n^2-n+2+(-1)^n.

Mathematica

s={0, 0, 1}; Do[AppendTo[s, Abs[s[[-1]]-s[[-2]]]+(-1)^n*s[[-3]]] , {n, 2, 76}]; s (* James C. McMahon, Sep 18 2024 *)

Crossrefs

Sequence in context: A333270 A333272 A352501 * A333450 A210112 A024735

Adjacent sequences: A119555 A119556 A119557 * A119559 A119560 A119561

Keyword

sign

Author

Benoit Cloitre, May 30 2006

Status

approved