%I
%S 1,2,2,6,13,25,51,102,208,411,823,1646,3296,6599,13210,26446,52943,
%T 105785,211571,423142,846288,1692583,3385178,6770382,13540815,
%U 27081736,54163675,108327762,216656347,433314344,866631991,1733270593
%N a(n) = a(1) + a(2) + ... + a(n1) + a(m) for n >= 4, where m = n  1  2^p 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.
%p s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n  1)); end proc:
%p a := proc(n) option remember; `if`(n < 4, [1, 2, 2][n], s(n  1) + a(2^ceil(log[2](n  1)  1) + n  1)); end proc:
%p seq(a(n), n = 1 .. 40); # _Petros Hadjicostas_, Apr 23 2020
%Y Cf. A049906 (similar, but with minus a(m)), A049907 (similar, but with minus a(2*m)), A049955 (similar, but with plus a(2*m)).
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Apr 23 2020
