A049950 - OEIS

%I #12 Apr 24 2020 02:10:16

%S 1,2,1,5,11,21,43,85,174,344,689,1377,2758,5522,11054,22130,44302,

%T 88520,177041,354081,708166,1416338,2832686,5665394,11330830,22661749,

%U 45323668,90647681,181296050,362593481,725189726,1450384984

%N a(n) = a(1) + a(2) + ... + a(n-1) + 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), with a(1) = 1, a(2) = 2, 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; `if`(n < 4, [1, 2, 1][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

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Apr 23 2020