%I #10 Nov 16 2019 03:28:59
%S 1,3,3,8,18,34,70,155,362,655,1312,2639,5330,10952,22854,49726,116976,
%T 211099,422200,844415,1688882,3378056,6757062,13518142,27053808,
%U 54201738,108708700,218684082,442436344,905169434,1891993760
%N a(n) = a(1) + a(2) + ... + 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) = 3.
%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, 3][n], s(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p end proc:
%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 15 2019
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Nov 15 2019