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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).

%I A111466 #15 Jan 11 2020 07:52:46
%S A111466 1,0,2,5,0,8,21,0,34,89,0,144,377,0,610,1597,0,2584,6765,0,10946,
%T A111466 28657,0,46368,121393,0,196418,514229,0,832040,2178309,0,3524578,
%U A111466 9227465,0,14930352,39088169,0,63245986,165580141,0,267914296,701408733,0,1134903170
%N 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).
%H A111466 Harvey P. Dale, <a href="/A111466/b111466.txt">Table of n, a(n) for n = 1..1000</a>
%H A111466 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,0,0,1).
%F A111466 a(3n+2) =0, a(3n) = F(3n), a(3n+1) = F(3n+2).
%F A111466 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
%p A111466 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
%t A111466 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 *)
%Y A111466 Cf. A000045, A008344.
%K A111466 easy,nonn
%O A111466 1,3
%A A111466 _Amarnath Murthy_, Aug 05 2005
%E A111466 More terms from _Emeric Deutsch_, Aug 11 2005