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A054880
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a(n)=3(9^n-1)/4.
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3
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0, 6, 60, 546, 4920, 44286, 398580, 3587226, 32285040, 290565366, 2615088300, 23535794706, 211822152360, 1906399371246, 17157594341220, 154418349070986, 1389765141638880, 12507886274749926
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of walks of length 2n+1 along the edges of a cube between two opposite vertices.
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FORMULA
| G.f.: (3/4)*1/(1-9*x)-(3/4)/(1-x).
sin(x)^3 = sum k=0, 1, ... (-1)^(k+1) * x^(2k+1)/(2k+1)! * a(k) - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 08 2001
a(n) = A015518(2n+1)-1 = (A046717(2n+1)-1)/2. - M. F. Hasler, Mar 20 2008
a(n)=9*a(n-1)+6 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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EXAMPLE
| a(1)=9*0+6=6; a(2)=9*6+6=60; a(3)=9*60+6=546; a(4)=9*546+6=4920 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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CROSSREFS
| {a(n)/6} for n>0 is A002452.
Sequence in context: A102232 A121113 A091710 * A186656 A122653 A136943
Adjacent sequences: A054877 A054878 A054879 * A054881 A054882 A054883
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KEYWORD
| nonn,walk
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AUTHOR
| Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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