Every Other Fibonacci Number Sequence

9/20/2015

Here is an interesting sequence I ran across.  I was trying new numbers to see if I could find something new.  When I typed the first few terms into OEIS it brought me to this sequence.

Every Other Fibonacci Number (F(2*n)): a(0) = 0, a(1) = 1, and when n>1 then a(n) =3 * a(n-1) - a(n-2). This produces a list of the odd numbered terms in the Fibonacci Sequence.  (I working on, but have not found a way to do the even numbered terms) 999,997,000,001. 1/999997000001 = 0. 000000  000001  000003  000008  000021  000055  000144  000377  000987  002584  006765  017711  046368  121393  317811  … Written in six digit strings. Accurate to the 14th non-zero term. Compare OEIS sequence A001906.

David