%I #11 Nov 13 2019 01:38:58

%S 1,3,1,2,6,11,23,44,90,137,295,602,1209,2422,4845,9688,19378,29069,

%T 62981,128385,257983,516573,1033453,2067064,4134175,8268396,16536813,

%U 33073638,66147281,132294566,264589133,529178264,1058356530

%N a(n) = a(1) + a(2) + ... + 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) = 3, and a(3) = 1.

%p s:= proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:

%p a := proc(n) option remember;

%p `if`(n < 4, [1, 3, 1][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):

%p end proc:

%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 12 2019

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Nov 12 2019