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A049933 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) = a(3) = 1. 9
1, 1, 1, 4, 8, 19, 35, 70, 140, 349, 663, 1310, 2609, 5214, 10425, 20850, 41700, 104249, 198073, 390935, 779265, 1557231, 3113815, 6227316, 12454423, 24908776, 49817517, 99635018, 199270025, 398540046, 797080089, 1594160178, 3188320356, 7970800889, 15144521689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

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) = 4.

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) = 8.

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) = 19.

a(7) =  a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = a(3) +  Sum_{i = 1..6} a(i) = 35.

a(8) =  a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = a(2) +  Sum_{i = 1..7} a(i) = 70. (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 < 4, 1, s(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n));

end proc;

seq(a(n), n = 1 .. 30);

MATHEMATICA

b[n_] := Module[{p}, For[p = 0, True, p++, If[2^p < n - 1 <= 2^(p + 1), Return[p]]]];

a[n_] := a[n] = If[n < 4, 1, With[{m = 2^(b[n] + 1) + 2 - n}, Total[ Array[a, n - 1]] + a[m]]];

Array[a, 35] (* Jean-Fran├žois Alcover, Apr 24 2020 *)

CROSSREFS

Cf. A006257, A049885 (similar with minus a(m)), A049937, A049945.

Sequence in context: A162362 A274817 A130887 * A301746 A163318 A129362

Adjacent sequences:  A049930 A049931 A049932 * A049934 A049935 A049936

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

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

STATUS

approved

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Last modified January 25 11:03 EST 2022. Contains 350567 sequences. (Running on oeis4.)