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A049909 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 smallest integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 3.

%I A049909 #19 Nov 12 2019 08:36:04
%S A049909 1,2,3,4,9,15,31,63,127,192,416,848,1702,3409,6819,13639,27279,40920,
%T A049909 88660,180730,363167,727188,1454808,2909840,5819745,11639554,23279140,
%U A049909 46558296,93116598,186233201,372466403,744932807,1489865615
%N A049909 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 smallest integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 3.
%F A049909 From _Petros Hadjicostas_, Nov 07 2019: (Start)
%F A049909 a(n) = -a(2^ceiling(log_2(n-1)) + 2 - n) + Sum_{i = 1..n-1} a(i) for n >= 4.
%F A049909 a(n) = -a(n - 1 - A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4. (End)
%e A049909 From _Petros Hadjicostas_, Nov 07 2019: (Start)
%e A049909 a(4) = -a(2^ceiling(log_2(4-1)) + 2 - 4) + a(1) + a(2) + a(3) = -a(2) + a(1) + a(2) + a(3) = 4.
%e A049909 a(5) = -a(2^ceiling(log_2(5-1)) + 2 - 5) + a(1) + a(2) + a(3) + a(4) = -a(1) + a(1) + a(2) + a(3) + a(4) = 9.
%e A049909 a(6) = -a(2^ceiling(log_2(6-1)) + 2 - 6) + a(1) + a(2) + a(3) + a(4) + a(5) = -a(4) + a(1) + a(2) + a(3) + a(4) + a(5) = 15.
%e A049909 a(7) =  -a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = -a(3) +  Sum_{i = 1..6} a(i) = 31.
%e A049909 a(8) =  -a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = -a(2) +  Sum_{i = 1..7} a(i) = 63. (End)
%p A049909 s:= proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end:
%p A049909 a:= proc(n) option remember; `if`(n<4, [1, 2, 3][n],
%p A049909       s(n-1) - a(Bits:-Iff(n-2$2) + 3 - n))
%p A049909     end:
%p A049909 seq(a(n), n=1..40); # _Petros Hadjicostas_, Nov 07 2019
%Y A049909 Cf. A006257, A049933, A049937, A049945, A049977.
%K A049909 nonn
%O A049909 1,2
%A A049909 _Clark Kimberling_
%E A049909 Name edited by _Petros Hadjicostas_, Nov 07 2019