A049979 a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) 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, 30, 52, 112, 265, 743, 1224, 2456, 4953, 10119, 21197, 46123, 108490, 304273, 500059, 1000126, 2000293, 4000799, 8002557, 16008843, 32033930, 64155153, 128701875, 258903984, 523810232, 1071651837, 2239971619

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = a(1 + A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4 with a(1) = 1, a(2) = 3, and a(3) = 4. - Petros Hadjicostas, Sep 24 2019

Example

From Petros Hadjicostas, Sep 24 2019: (Start)
a(4) = a(1 + A006257(4-2)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 3 + 1 + 3 + 4 = 11.
a(7) = a(1 + A006257(7-2)) + a(1) + ... + a(6) = a(4) + a(1) + ... + a(6) = 11 + 1 + 3 + 4 + 11 + 30 + 52 = 112.
(End)

Maple

a := proc(n) local i; option remember; if n < 4 then return [1, 3, 4][n]; end if; add(a(i), i = 1 .. n - 1) + a(2*n - 3 - Bits:-Iff(n - 2, n - 2)); end proc;
seq(a(n), n = 1 .. 37); # Petros Hadjicostas, Sep 24 2019, courtesy of Peter Luschny

Crossrefs

Cf. A006257, A049939, A049940, A049960, A049964.

Sequence in context: A180363 A100845 A019169 * A084378 A038559 A242044

Adjacent sequences: A049976 A049977 A049978 * A049980 A049981 A049982

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Sep 24 2019

Status

approved