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A330513 a(n) = a(n-1) + a(floor(n/4)), a(1)=a(2)=a(3) = 1.

%I A330513 #13 Mar 05 2020 02:40:48
%S A330513 1,1,1,2,3,4,5,6,7,8,9,10,11,12,13,15,17,19,21,24,27,30,33,37,41,45,
%T A330513 49,54,59,64,69,75,81,87,93,100,107,114,121,129,137,145,153,162,171,
%U A330513 180,189,199,209,219,229,240,251,262,273,285,297,309,321,334,347
%N A330513 a(n) = a(n-1) + a(floor(n/4)), a(1)=a(2)=a(3) = 1.
%C A330513 Also the number of finite sequences b(1..r) satisfying the conditions b(1) = 1, b(i+1) >= 4 b(i) for 1 <= i < r, and b(r) <= n.
%H A330513 Michael De Vlieger, <a href="/A330513/b330513.txt">Table of n, a(n) for n = 1..10000</a>
%H A330513 Lukas Fleischer, Samin Riasat, Jeffrey Shallit, <a href="https://arxiv.org/abs/1912.08147">New Bounds on Antipowers in Binary Words</a>, arXiv:1912.08147 [cs.FL], 2019.
%p A330513 a:= proc(n) option remember;
%p A330513      `if`(n<4, signum(n), a(n-1)+a(iquo(n, 4)))
%p A330513     end:
%p A330513 seq(a(n), n=1..75);  # _Alois P. Heinz_, Dec 16 2019
%t A330513 Nest[Append[#1, #1[[-1]] + #1[[Floor[#2/4] ]] ] & @@ {#, Length@ # + 1} &, {1, 1, 1}, 58] (* _Michael De Vlieger_, Mar 04 2020 *)
%Y A330513 Cf. A033485, A330500.
%K A330513 nonn
%O A330513 1,4
%A A330513 _Jeffrey Shallit_, Dec 16 2019