A049937 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), starting with a(1) = a(2) = 1 and a(3) = 2.

1, 1, 2, 5, 10, 24, 45, 89, 178, 444, 844, 1667, 3320, 6635, 13267, 26533, 53066, 132664, 252062, 497492, 991669, 1981685, 3962547, 7924694, 15849122, 31698155, 63396266, 126792511, 253585008, 507170011, 1014340019, 2028680037, 4057360074, 10143400184, 19272460350, 38037750692

Offset

1,3

Links

Table of n, a(n) for n=1..36.

Formula

From Petros Hadjicostas, Nov 06 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 06 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) = 5.
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) = 10.
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) = 24.
a(7) =  a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = a(3) +  Sum_{i = 1..6} a(i) = 45.
a(8) =  a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = a(2) +  Sum_{i = 1..7} a(i) = 89. (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 < 3, 1, `if`(n < 4, 2, s(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n)));
end proc;
seq(a(n), n = 1 .. 30); # Petros Hadjicostas, Nov 06 2019

Crossrefs

Cf. A006257, A049933, A049945.

Sequence in context: A112855 A361505 A299436 * A026754 A291247 A316697

Adjacent sequences: A049934 A049935 A049936 * A049938 A049939 A049940

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 06 2019

Status

approved