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A050044 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 and a(2) = a(3) = 2.

%I A050044 #16 Nov 15 2019 03:29:41
%S A050044 1,2,2,3,5,6,8,13,21,22,24,29,37,58,82,119,201,202,204,209,217,238,
%T A050044 262,299,381,582,786,1003,1265,1646,2432,3697,6129,6130,6132,6137,
%U A050044 6145,6166,6190,6227,6309,6510,6714,6931,7193,7574,8360
%N A050044 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 and a(2) = a(3) = 2.
%H A050044 Ivan Neretin, <a href="/A050044/b050044.txt">Table of n, a(n) for n = 1..8193</a>
%p A050044 a := proc(n) option remember;
%p A050044 `if`(n < 4, [1, 2, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p A050044 end proc:
%p A050044 seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019
%t A050044 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 2}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050044 Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), 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 A050044 nonn
%O A050044 1,2
%A A050044 _Clark Kimberling_
%E A050044 Name edited by _Petros Hadjicostas_, Nov 14 2019