A049945 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) = 4.

1, 1, 4, 7, 14, 34, 65, 127, 254, 634, 1206, 2381, 4742, 9477, 18951, 37899, 75798, 189494, 360040, 710606, 1416477, 2830593, 5660011, 11319450, 22638520, 45276913, 90553764, 181107497, 362214974, 724429941, 1448859879, 2897719755, 5795439510, 14488598774, 27528337672, 54332245406

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) = 7.
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) = 14.
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) = 34.
a(7) =  a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = a(3) +  Sum_{i = 1..6} a(i) = 65.
a(8) =  a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = a(2) +  Sum_{i = 1..7} a(i) = 127. (End)

Maple

s:= proc(n) option remember; `if`(n<1, 0, a(n)+s(n-1)) end:
a:= proc(n) option remember; `if`(n<4, [1, 1, 4][n],
      s(n-1)+a(Bits:-Iff(n-2$2)+3-n))
    end:
seq(a(n), n=1..36); # Petros Hadjicostas, Nov 06 2019

Crossrefs

Cf. A006257, A049933, A049937.

Sequence in context: A050343 A245002 A199628 * A234576 A076586 A240266

Adjacent sequences: A049942 A049943 A049944 * A049946 A049947 A049948

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved