

A147610


a(n) = 3^{wt(n1)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
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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(n2).  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


CROSSREFS

Cf. A048883, A000120, A000302, A151920, A147582, A048881.
Cf. A079314.  Omar E. Pol, Nov 15 2009
Sequence in context: A327190 A160123 A238784 * 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



