A111466 a(1) = 1, a(n+1) = a(n) - F(n+1), if F(n+1) <= a(n), else a(n+1) = a(n) + F(n+1). F(n) is the n-th Fibonacci number (A000045).

1, 0, 2, 5, 0, 8, 21, 0, 34, 89, 0, 144, 377, 0, 610, 1597, 0, 2584, 6765, 0, 10946, 28657, 0, 46368, 121393, 0, 196418, 514229, 0, 832040, 2178309, 0, 3524578, 9227465, 0, 14930352, 39088169, 0, 63245986, 165580141, 0, 267914296, 701408733, 0, 1134903170

Offset: 1

Author

Amarnath Murthy, Aug 05 2005

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,1).

Crossrefs

Cf. A000045, A008344.

Programs

Maple

with(combinat): a[1]:=1: for n from 1 to 50 do if fibonacci(n+1)<=a[n] then a[n+1]:=a[n]-fibonacci(n+1) else a[n+1]:=a[n]+fibonacci(n+1) fi od: seq(a[n],n=1..51); # Emeric Deutsch, Aug 11 2005

Mathematica

nxt[{n_,a_}]:=Module[{fib=Fibonacci[n+1]},{n+1,If[fib<=a,a-fib,a+fib]}]; Transpose[NestList[nxt,{1,1},50]][[2]] (* Harvey P. Dale, Nov 21 2012 *)

Formula

a(3n+2) =0, a(3n) = F(3n), a(3n+1) = F(3n+2).

G.f.: -x*(1+2*x^2+x^3) / ( (x^2+x-1)*(x^4-x^3+2*x^2+x+1) ). - R. J. Mathar, Jun 23 2014

Extensions

More terms from Emeric Deutsch, Aug 11 2005