A049977 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), with a(1) = 1, a(2) = 3, and a(3) = 4.

1, 3, 4, 11, 20, 50, 93, 185, 368, 920, 1748, 3453, 6876, 13743, 27479, 54957, 109912, 274780, 522082, 1030428, 2053989, 4104555, 8207405, 16413982, 32827412, 65654641, 131309190, 262618337, 525236644, 1050473279, 2100946551, 4201893101, 8403786200, 21009465500, 39917984450

Offset

1,2

Links

Table of n, a(n) for n=1..35.

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) = 11.
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) = 20.
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) = 50.
a(7) =  a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = a(3) +  Sum_{i = 1..6} a(i) = 93.
a(8) =  a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = a(2) +  Sum_{i = 1..7} a(i) = 185. (End)

Maple

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

Crossrefs

Cf. A006257, A049933, A049937, A049945.

Sequence in context: A036652 A295962 A097072 * A000677 A110865 A152982

Adjacent sequences: A049974 A049975 A049976 * A049978 A049979 A049980

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 07 2019

Status

approved