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A147610
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a(n) = 3^{wt(n-1)-1}, where wt() = A000120().
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14
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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
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2,3
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COMMENTS
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a(n) = A147582(n)/4.
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LINKS
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Table of n, a(n) for n=2..89.
O. E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol, Nov 15 2009]
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FORMULA
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a(n) = 3^A048881(n-2). [From 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*(Prod_{k>=0} (1+3*x^(2^k)) - 1)/3. - N. J. A. Sloane, Jun 10 2009
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EXAMPLE
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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.
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MAPLE
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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) ; [From R. J. Mathar, Apr 30 2009]
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CROSSREFS
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Cf. A048883, A000120, A000302, A151920, A147582, A048881.
Cf. A079314. [From Omar E. Pol, Nov 15 2009]
Sequence in context: A151837 A163381 A160123 * A133579 A163270 A098743
Adjacent sequences: A147607 A147608 A147609 * A147611 A147612 A147613
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 29 2009
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EXTENSIONS
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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
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STATUS
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approved
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