A224382 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.

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, 155, 69, 14, 83, 97, 45, 142, 187, 329, 129, 458, 587, 1045, 102, 1147, 1249, 599, 462, 1061, 1523, 646, 2169, 2815, 1246, 4061, 5307, 2342, 7649, 9991, 4410

Offset: 0

Author

Vladimir Shevelev, Apr 05 2013

Keywords

• nonn

Links

• Peter J. C. Moses, Table of n, a(n) for n = 0..9999
• B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5

Crossrefs

Cf. A000045, A078414, A214094, A214156, A216231, A216275, A216835.

Programs

Mathematica

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 *)