A166267 Number of 1's in the binary representation of A000129(n).

0, 1, 1, 2, 2, 4, 3, 4, 4, 7, 5, 8, 6, 7, 10, 11, 10, 8, 13, 12, 12, 14, 16, 17, 11, 14, 17, 20, 16, 17, 19, 21, 23, 17, 17, 19, 24, 24, 25, 18, 29, 26, 29, 26, 26, 29, 35, 29, 26, 40, 29, 33, 33, 38, 36, 34, 28, 38, 42, 40, 37, 34, 40, 27, 45, 35, 37, 41, 40, 44, 48, 45, 41, 45

Offset

0,4

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000120(A000129(n)). - R. J. Mathar, Oct 28 2009

Mathematica

Clear[a, b, c, f, n, lst] f[n_]:=Plus@@IntegerDigits[n, 2]; a=1; b=0; c=0; lst={b}; Do[c=a+b+c; AppendTo[lst, f[c]]; a=b; b=c, {n, 5!}]; lst
DigitCount[LinearRecurrence[{2, 1}, {0, 1}, 100], 2, 1] (* Amiram Eldar, Jul 29 2023 *)

Prog

(Python)
def A000129(n):
    if n <=1:
        return n
    else:
        return 2*A000129(n-1)+A000129(n-2)
def A000120(n):
    a=0
    sh=n
    while sh > 0:
        a += sh & 1
        sh >>= 1
    return a
def A166267(n):
    return A000120(A000129(n))
print([A166267(n) for n in range(30)])
# R. J. Mathar, Oct 18 2009

Crossrefs

Cf. A000120, A000129.

Sequence in context: A094950 A087874 A363341 * A117484 A086835 A046701

Adjacent sequences: A166264 A166265 A166266 * A166268 A166269 A166270

Keyword

nonn,base,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 10 2009

Extensions

Keyword:base added by R. J. Mathar, Oct 28 2009

Offset changed to 0 by Georg Fischer, Dec 19 2020

Status

approved