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A050040 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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 A050040 #17 Nov 15 2019 03:29:31
%S A050040 1,2,1,2,3,4,5,8,13,14,15,18,23,36,51,74,125,126,127,130,135,148,163,
%T A050040 186,237,362,489,624,787,1024,1513,2300,3813,3814,3815,3818,3823,3836,
%U A050040 3851,3874,3925,4050,4177,4312,4475,4712,5201
%N A050040 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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 A050040 Ivan Neretin, <a href="/A050040/b050040.txt">Table of n, a(n) for n = 1..8193</a>
%p A050040 a := proc(n) option remember;
%p A050040 `if`(n < 4, [1, 2, 1][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p A050040 end proc:
%p A050040 seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019
%t A050040 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050040 Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).
%K A050040 nonn
%O A050040 1,2
%A A050040 _Clark Kimberling_
%E A050040 Name edited by _Petros Hadjicostas_, Nov 14 2019