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A050053 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 4.

%I A050053 #15 Nov 10 2019 01:32:32
%S A050053 1,2,4,6,7,13,17,19,20,39,56,69,76,82,86,88,89,177,263,345,421,490,
%T A050053 546,585,605,624,641,654,661,667,671,673,674,1347,2018,2685,3346,4000,
%U A050053 4641,5265,5870,6455,7001,7491,7912,8257,8520,8697
%N A050053 a(n) = a(n-1) + a(m) for n >= 4, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 4.
%H A050053 Ivan Neretin, <a href="/A050053/b050053.txt">Table of n, a(n) for n = 1..8193</a>
%p A050053 a := proc(n) option remember;
%p A050053 `if`(n < 4, [1, 2, 4][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
%p A050053 seq(a(n), n = 1 .. 48); # _Petros Hadjicostas_, Nov 09 2019
%t A050053 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 4}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y A050053 Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).
%K A050053 nonn
%O A050053 1,2
%A A050053 _Clark Kimberling_
%E A050053 Name edited by _Petros Hadjicostas_, Nov 09 2019