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A049941 a(n) = a(1) + a(2) + ... + a(n-1) + a(m), 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. 0
1, 1, 3, 6, 12, 29, 55, 108, 216, 539, 1025, 2024, 4031, 8056, 16109, 32216, 64432, 161079, 306051, 604049, 1204073, 2406139, 4811279, 9622072, 19243821, 38487534, 76975015, 153950004, 307899991, 615799976, 1231599949, 2463199896, 4926399792, 12315999479, 23400399011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

From Petros Hadjicostas, Oct 06 2019: (Start)

a(n) = a(2 - n + 2^ceiling(log_2(n-1))) + Sum_{i = 1..n-1} a(i) for n >= 3.

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

(End)

EXAMPLE

From Petros Hadjicostas, Oct 06 2019: (Start)

a(3) = a(2 - 3 + 2^ceiling(log_2(3-1))) + a(1) + a(2) = a(1) + a(1) + a(2) = 3.

a(4) = a(2 - 4 + 2^ceiling(log_2(4-1))) + a(1) + a(2) + a(3) =  a(2) + a(1) + a(2) + a(3) = 6.

a(5) = a(5 - 1 - A006257(5-2)) + a(1) + a(2) + a(3) + a(4) = a(1) + a(1) + a(2) + a(3) + a(4) = 12.

(End)

MAPLE

a := proc(n) local i; option remember; if n < 3 then return [1, 1][n]; end if; add(a(i), i = 1 .. n - 1) + a(3 - n + Bits:-Iff(n - 2, n - 2)); end proc;

seq(a(n), n = 1 .. 35); # Petros Hadjicostas, Oct 06 2019

CROSSREFS

Cf. A006257.

Sequence in context: A018011 A025208 A245774 * A219634 A252696 A288147

Adjacent sequences:  A049938 A049939 A049940 * A049942 A049943 A049944

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Petros Hadjicostas, Oct 06 2019

STATUS

approved

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Last modified October 18 19:15 EDT 2021. Contains 348069 sequences. (Running on oeis4.)