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.

1, 2, 3, 4, 9, 15, 31, 63, 127, 192, 416, 848, 1702, 3409, 6819, 13639, 27279, 40920, 88660, 180730, 363167, 727188, 1454808, 2909840, 5819745, 11639554, 23279140, 46558296, 93116598, 186233201, 372466403, 744932807, 1489865615

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Formula

From Petros Hadjicostas, Nov 07 2019: (Start)

a(n) = -a(2^ceiling(log_2(n-1)) + 2 - n) + Sum_{i = 1..n-1} a(i) for n >= 4.

a(n) = -a(n - 1 - A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4. (End)

Example

From Petros Hadjicostas, Nov 07 2019: (Start)
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.
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.
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.
a(7) =  -a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = -a(3) +  Sum_{i = 1..6} a(i) = 31.
a(8) =  -a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = -a(2) +  Sum_{i = 1..7} a(i) = 63. (End)

Maple

s:= proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end:
a:= proc(n) option remember; `if`(n<4, [1, 2, 3][n],
      s(n-1) - a(Bits:-Iff(n-2$2) + 3 - n))
    end:
seq(a(n), n=1..40); # Petros Hadjicostas, Nov 07 2019

Crossrefs

Cf. A006257, A049933, A049937, A049945, A049977.

Sequence in context: A124753 A248647 A284437 * A346211 A096781 A232055

Adjacent sequences: A049906 A049907 A049908 * A049910 A049911 A049912

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Nov 07 2019

Status

approved