A133147 a(n) = a(n-1) + Sum_{k=0..floor(log_2(n-1))} a(2^k), a(1) = 1.

1, 2, 5, 8, 19, 30, 41, 52, 115, 178, 241, 304, 367, 430, 493, 556, 1175, 1794, 2413, 3032, 3651, 4270, 4889, 5508, 6127, 6746, 7365, 7984, 8603, 9222, 9841, 10460, 21539, 32618, 43697, 54776, 65855, 76934, 88013, 99092, 110171, 121250, 132329

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Example

a(7)  = a(6) + a(1)+a(2)+a(4)      =  30 + 1+2+8    =  41;
a(8)  = a(7) + a(1)+a(2)+a(4)      =  41 + 1+2+8    =  52;
a(9)  = a(8) + a(1)+a(2)+a(4)+a(8) =  52 + 1+2+8+52 = 115;
a(10) = a(9) + a(1)+a(2)+a(4)+a(8) = 115 + 1+2+8+52 = 178.

Mathematica

a[1]=1; a[n_]:=a[n-1]+Sum[a[2^k], {k, 0, Floor[Log2[n-1]]}]; Table[a[n], {n, 43}] (* James C. McMahon, Mar 11 2025 *)

Crossrefs

Sequence in context: A256723 A032063 A320426 * A358828 A082630 A025078

Adjacent sequences: A133144 A133145 A133146 * A133148 A133149 A133150

Keyword

nonn

Author

Reinhard Zumkeller, Dec 16 2007

Status

approved