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A147610 a(n) = 3^(wt(n-1)-1), where wt() = A000120(). 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
a(n) = A147582(n)/4.
LINKS
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
EXAMPLE
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.
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 *)
PROG
(PARI) a(n) = 3^(hammingweight(n-1)-1); \\ Michel Marcus, Mar 24 2020
CROSSREFS
Cf. A079314. - Omar E. Pol, Nov 15 2009
Sequence in context: A160123 A238784 A336765 * A238313 A163270 A098743
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 29 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
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)