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%I #27 Apr 03 2015 18:01:43
%S 1,1,21,2,8,34,1597,3,6765,13,610,55,55,2584,2584,5,233,10946,10946,
%T 21,21,987,987,89,46368,89,114059301025943970552219,4181,4181,4181,
%U 10284720757613717413913,8,196418,377,377,17711,17711,17711,9227465,34
%N Collatz-Fibonacci numbers: a(1) = a(2) = 1; if n > 2, a(n) = a(C(n)) + a(C(C(n))), where C(n) = A006370(n).
%H Reinhard Zumkeller, <a href="/A174429/b174429.txt">Table of n, a(n) for n = 1..10000</a>
%H Sam Alexander, <a href="http://www.xamuel.com/collatz-recursion/">Collatz Recursion</a>
%F a(n) = Fibonacci(A008908(n)) = A000045(A008908(n)). - _T. D. Noe_, Jul 06 2010
%e a(4) = a(2) + a(1) = 2. a(8) = a(4) + a(2) = 3. a(16) = a(8) + a(4) = 5. a(5) = a(16) + a(8) = 8.
%t collatz[n_] := If[EvenQ[n], n/2, 3n + 1]; collFibo[1] = 1; collFibo[2] = 1; collFibo[n_] := collFibo[n] = collFibo[collatz[n]] + collFibo[collatz[collatz[n]]]; Table[collFibo[n], {n, 100}] (* _T. D. Noe_, Jul 06 2010 *)
%o (Haskell)
%o a174429 = a000045 . a008908 -- _Reinhard Zumkeller_, Nov 10 2011
%K nonn,nice,look
%O 1,3
%A _Sam Alexander_, Mar 19 2010
%E Corrected by _T. D. Noe_, Jul 06 2010
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