A147610 a(n) = 3^(wt(n-1)-1), where wt() = A000120().
1, 1, 3, 1, 3, 3, 9, 1, 3, 3, 9, 3, 9, 9, 27, 1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27, 9, 27, 27, 81, 1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27, 9, 27, 27, 81, 3, 9, 9, 27, 9, 27, 27, 81, 9, 27, 27, 81, 27, 81, 81, 243, 1, 3, 3, 9, 3, 9, 9, 27, 3, 9, 9, 27, 9, 27, 27, 81, 3, 9, 9, 27, 9, 27, 27, 81, 9
Offset: 2
Keywords
Examples
When written as a triangle: .1, .1,3, .1,3,3,9, .1,3,3,9,3,9,9,27, .1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81, .1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,3,9,9,27,9,27,27,81,9,27,27,81,27,81,81,243, .... Rows converge to A048883. Row sums give A000302. Partial sums give A151920.
Links
- Omar E. Pol, Illustration of initial terms (Overlapping squares) [From _Omar E. Pol_, Nov 15 2009]
Crossrefs
Programs
-
Maple
A000120 := proc(n) local a,d; a := 0 ; for d from 0 to ilog2(n) do a := a+ ( floor(n/2^d) mod 2) ; od: a ; end: A048881 := proc(n) A000120(n+1)-1 ; end: A147610 := proc(n) 3^A048881(n) ; end: seq(A147610(n),n=0..100) ; # R. J. Mathar, Apr 30 2009
-
Mathematica
a[n_] := 3^(DigitCount[n - 1, 2, 1] - 1); a /@ Range[2, 100] (* Jean-François Alcover, Mar 24 2020 *)
-
PARI
a(n) = 3^(hammingweight(n-1)-1); \\ Michel Marcus, Mar 24 2020
Formula
a(n) = 3^A048881(n-2). - R. J. Mathar, Apr 30 2009
Recurrence: Write n = 2^i + 1 + j, 0 <= j < 2^i. Then a(2^i+1) = 1; for j>0, a(2^i+j+1) = 3*a(j+1). - N. J. A. Sloane, Jun 09 2009
G.f.: x*(Product_{k>=0} (1 + 3*x^(2^k)) - 1)/3. - N. J. A. Sloane, Jun 10 2009
Extensions
Extended by R. J. Mathar, Apr 30 2009
Offset corrected by N. J. A. Sloane, Jun 09 2009
Further edited by N. J. A. Sloane, Aug 06 2009
Comments