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A305876 a(n) = Fibbinary(2^n).

%I A305876 #21 Jun 14 2018 15:29:19
%S A305876 1,2,5,16,36,84,273,648,2114,4757,16516,37161,87045,282896,673924,
%T A305876 2184233,5263877,17107472,38830244,134554132,303080705,707272770,
%U A305876 2300725397,5457925252,17805431433,42970665029,139654661284,314223120404,1099646108737,2474203744786
%N A305876 a(n) = Fibbinary(2^n).
%H A305876 Alois P. Heinz, <a href="/A305876/b305876.txt">Table of n, a(n) for n = 0..2306</a>
%F A305876 a(n) = A003714(2^n).
%F A305876 A014417(2^n) = A007088(a(n)).
%e A305876 a(6) = A003714(2^6) = A003714(64) = 273 = 100010001_2 because F(0+2) + F(4+2) + F(8+2) = 1 + 8 + 55 = 64, where 0, 4, 8 are the indices of 1 bits in 100010001_2.  A014417(64) = 100010001 = A007088(273).
%p A305876 F:= proc(n) F(n):= `if`(n<2, n, F(n-1)+F(n-2)) end:
%p A305876 b:= proc(n) local j;
%p A305876       if n=0 then 0
%p A305876     else for j from 2 while F(j+1)<=n do od;
%p A305876          b(n-F(j))+2^(j-2)
%p A305876       fi
%p A305876     end:
%p A305876 a:= n-> b(2^n):
%p A305876 seq(a(n), n=0..35);
%o A305876 (Python)
%o A305876 def A305876(n):
%o A305876     m, tlist, s = 2**n, [1,2], 0
%o A305876     while tlist[-1]+tlist[-2] <= m:
%o A305876         tlist.append(tlist[-1]+tlist[-2])
%o A305876     for d in tlist[::-1]:
%o A305876         s *= 2
%o A305876         if d <= m:
%o A305876             s += 1
%o A305876             m -= d
%o A305876     return s # _Chai Wah Wu_, Jun 14 2018
%Y A305876 Cf. A000045, A000079, A003714 (Fibbinary), A007088, A014417, A305380.
%K A305876 nonn,base
%O A305876 0,2
%A A305876 _Alois P. Heinz_, Jun 12 2018