A049939 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) = a(2) = 1 and a(3) = 2.

1, 1, 2, 5, 14, 24, 52, 123, 345, 568, 1140, 2299, 4697, 9839, 21409, 50358, 141235, 232113, 464230, 928479, 1857057, 3714559, 7430849, 14869238, 29778995, 59739745, 120175856, 243137792, 497430263, 1039731033, 2262860113

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

a(n) = a(1 + A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4 with a(1) = a(2) = 1 and a(3) = 2.

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) = 1 + 1 + 1 + 2 = 5.
a(5) = a(1 + A006257(5-2)) + a(1) + a(2) + a(3) + a(4) = a(4) + a(1) + a(2) + a(3) + a(4) = 5 + 1 + 1 + 2 + 5 = 14.
a(6) = a(1 + A006257(6-2)) + a(1) + a(2) + a(3) + a(4) + a(5) = a(2) +  a(1) + a(2) + a(3) + a(4) + a(5) = 1 + 1 + 1 + 2 + 5 + 14 = 24.
(End)

Maple

a := proc(n) local i; option remember; if n < 4 then return [1, 1, 2][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, A049890 (similar, but with minus a(m/2)), A049891 (similar, but with minus a(m)), A049938 (similar, but with plus a(m/2)), A049940, A049960, A049964.

Sequence in context: A321287 A076664 A220477 * A296302 A240401 A133375

Adjacent sequences: A049936 A049937 A049938 * A049940 A049941 A049942

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Sep 24 2019

Status

approved