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A050041 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) = 1.

%I A050041 #16 Nov 12 2019 09:01:07
%S A050041 1,2,1,3,4,7,8,10,11,21,29,36,40,43,44,46,47,93,137,180,220,256,285,
%T A050041 306,317,327,335,342,346,349,350,352,353,705,1055,1404,1750,2092,2427,
%U A050041 2754,3071,3377,3662,3918,4138,4318,4455,4548,4595
%N A050041 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) = 1.
%H A050041 Ivan Neretin, <a href="/A050041/b050041.txt">Table of n, a(n) for n = 1..8193</a>
%p A050041 a := proc(n) option remember;
%p A050041 `if`(n < 4, [1, 2, 1][n], a(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)); end proc;
%p A050041 seq(a(n), n = 1..50); # _Petros Hadjicostas_, Nov 11 2019
%t A050041 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050041 Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3), A050069 (1,3,4).
%K A050041 nonn
%O A050041 1,2
%A A050041 _Clark Kimberling_
%E A050041 Name edited by _Petros Hadjicostas_, Nov 11 2019