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A062188 a(n+1) = a(n) + a(floor(n/2)), with a(0)=0, a(1)=1.

%I A062188 #16 Sep 08 2022 08:45:03
%S A062188 0,1,1,2,3,4,5,7,9,12,15,19,23,28,33,40,47,56,65,77,89,104,119,138,
%T A062188 157,180,203,231,259,292,325,365,405,452,499,555,611,676,741,818,895,
%U A062188 984,1073,1177,1281,1400,1519,1657,1795,1952,2109,2289,2469,2672,2875,3106
%N A062188 a(n+1) = a(n) + a(floor(n/2)), with a(0)=0, a(1)=1.
%H A062188 Ivan Neretin, <a href="/A062188/b062188.txt">Table of n, a(n) for n = 0..10000</a>
%F A062188 G.f. A(x) satisfies: A(x) = x * (1 + (1 + x)*A(x^2))/(1 - x). - _Ilya Gutkovskiy_, May 04 2019
%e A062188 a(6) = a(5)+a(2) = 4+1 = 5.
%e A062188 a(7) = a(6)+a(3) = 5+2 = 7.
%t A062188 Join[{0}, Nest[Append[#, #[[-1]] + #[[Quotient[Length@#, 2]]]] &, {1, 1}, 53]] (* _Ivan Neretin_, Mar 03 2016 *)
%o A062188 (Magma) [n le 2 select n-1 else  Self(n-1)+Self(Floor(n/2)): n in [1..60]]; // _Vincenzo Librandi_, Mar 03 2016
%o A062188 (Python)
%o A062188 from itertools import islice
%o A062188 from collections import deque
%o A062188 def A062188_gen(): # generator of terms
%o A062188     aqueue, f, b, a = deque([1]), True, 0, 1
%o A062188     yield from (0,1)
%o A062188     while True:
%o A062188         a += b
%o A062188         yield a
%o A062188         aqueue.append(a)
%o A062188         if f: b = aqueue.popleft()
%o A062188         f = not f
%o A062188 A062188_list = list(islice(A062188_gen(),40)) # _Chai Wah Wu_, Jun 08 2022
%Y A062188 Cf. A033485, A062186, A062187.
%K A062188 nonn
%O A062188 0,4
%A A062188 _Henry Bottomley_, Jun 13 2001