A151787 a(1)=1; for n > 1, a(n)=3*2^{wt(n-1)-1}.

1, 3, 3, 6, 3, 6, 6, 12, 3, 6, 6, 12, 6, 12, 12, 24, 3, 6, 6, 12, 6, 12, 12, 24, 6, 12, 12, 24, 12, 24, 24, 48, 3, 6, 6, 12, 6, 12, 12, 24, 6, 12, 12, 24, 12, 24, 24, 48, 6, 12, 12, 24, 12, 24, 24, 48, 12, 24, 24, 48, 24, 48, 48, 96, 3, 6, 6, 12, 6, 12, 12, 24, 6, 12, 12, 24, 12, 24, 24, 48

Offset: 1

Author

N. J. A. Sloane, Jun 25 2009

Keywords

• nonn

Comments

wt(n) is the Hamming weight = binary weight of n (A000120).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A001316, A147582, A151779.

Programs

Maple

wt:= n -> convert(convert(n,base,2),`+`):
[1, seq(3*2^(wt(n-1)-1),n=2..100)]; # Robert Israel, Feb 27 2018

Mathematica

a[n_] := If[n == 1, 1, 3*2^(Total[IntegerDigits[n-1, 2]]-1)];
Array[a, 100] (* Jean-François Alcover, Mar 27 2019 *)

PARI

a(n) = if (n==1, 1, 3*2^(hammingweight(n-1)-1)); \\ Michel Marcus, Feb 27 2018

Formula

From Robert Israel, Feb 27 2018: (Start)

For n > 1, a(2*n)=2*a(n).

a(2*n+1)=a(n+1).

G.f. g(x) satisfies g(x) = (2+1/x)*g(x^2) + x^2. (End)

a(n) = 3*A001316(n-1)/2 for n >= 2. - Georg Fischer, Jun 23 2021

Extensions

Definition corrected by Omar E. Pol, Mar 03 2015