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%I #18 Feb 28 2018 15:24:58
%S 0,1,1,2,3,5,2,7,9,1,10,11,21,2,23,25,3,7,10,17,27,11,38,49,87,34,121,
%T 155,69,14,83,97,45,142,187,329,129,458,587,1045,102,1147,1249,599,
%U 462,1061,1523,646,2169,2815,1246,4061,5307,2342,7649,9991,4410
%N Fibonacci-like numbers without positive multiples of 4: a(0) = 0, a(1) = 1, for n>=2, a(n) = a(n-1) + a(n-2) divided by maximal possible power of 4.
%H Peter J. C. Moses, <a href="/A224382/b224382.txt">Table of n, a(n) for n = 0..9999</a>
%H B. Avila and T. Khovanova, <a href="http://arxiv.org/abs/1403.4614">Free Fibonacci Sequences</a>, arXiv preprint arXiv:1403.4614, 2014 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Avila/avila4.html">J. Int. Seq. 17 (2014) # 14.8.5</a>
%t a[0]:=0; a[1]:=1; a[n_]:=a[n]=#/4^IntegerExponent[#,4]&[(a[n-1]+a[n-2])]; Map[a,Range[0,99]] (* _Peter J. C. Moses_, Apr 05 2013 *)
%Y Cf. A000045, A078414, A214094, A214156, A216231, A216275, A216835.
%K nonn
%O 0,4
%A _Vladimir Shevelev_, Apr 05 2013
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