[math-fun] A fractal seq +/- 2007

Hello Math-Fun, if you erase all terms hereunder which are the sum of the two previous terms, you'll get the original sequence. Will the term 2007 appear some time? And if yes, at what index? Best, É. 0,1,1,1,1,2,1,2,3,1,2,3,3,1,4,2,3,5,3,1,4,4,2,6,3,5,8,3,1,4,4,4,8,2,6,8,3,5,8,8,3,11,1,4,5,4,4,8,8,2,10,6,8,14,3,5,8,... - - - - - - - - - - - - - -- - - -- -- -