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

2,3

Comments

a(n) = A147582(n)/4.

Links

Table of n, a(n) for n=2..89.

Omar E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol, Nov 15 2009]

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. A048883, A000120, A000302, A151920, A147582, A048881.

Cf. A079314. - Omar E. Pol, Nov 15 2009

Sequence in context: A160123 A238784 A336765 * A238313 A163270 A098743

Adjacent sequences: A147607 A147608 A147609 * A147611 A147612 A147613

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