A174562 a(1)=2, a(2)=3, then a(n)=a(n-1)+a(n-2) if n odd, a(n)=a(n-1)-a(n-2) if n even.

2, 3, 5, 2, 7, 5, 12, 7, 19, 12, 31, 19, 50, 31, 81, 50, 131, 81, 212, 131, 343, 212, 555, 343, 898, 555, 1453, 898, 2351, 1453, 3804, 2351, 6155, 3804, 9959, 6155, 16114, 9959, 26073, 16114, 42187, 26073, 68260, 42187, 110447, 68260, 178707, 110447

Offset: 1

Author

Giovanni Teofilatto, Mar 22 2010

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

Programs

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,If[EvenQ[n],b-a,b+a]}; Transpose[ NestList[ nxt,{1,2,3},50]][[2]] (* or *) LinearRecurrence[{0,1,0,1},{2,3,5,2},51] (* Harvey P. Dale, Jan 06 2012 *)

Formula

a(n)= a(n-2) +a(n-4). G.f.: x*(-2-3*x-3*x^2+x^3)/(-1+x^2+x^4). a(2n+1) = A001060(n). a(2n) = A013655(n-1). [From R. J. Mathar, Apr 14 2010]

Extensions

a(44) corrected by R. J. Mathar, Apr 14 2010

Precise definition from R. J. Mathar, Aug 23 2010