A147610 - OEIS

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

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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