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Search: id:A054880
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| 0, 6, 60, 546, 4920, 44286, 398580, 3587226, 32285040, 290565366, 2615088300, 23535794706, 211822152360, 1906399371246, 17157594341220, 154418349070986, 1389765141638880, 12507886274749926
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OFFSET
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0,2
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COMMENT
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Number of walks of length 2n+1 along the edges of a cube between two opposite vertices.
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FORMULA
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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(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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EXAMPLE
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For n=2, a(2)=9*0+6=6; n=3, a(3)=9*6+6=60; n=4, a(4)=9*60+6=546 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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CROSSREFS
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{a(n)/6} for n>0 is A002452.
Sequence in context: A102232 A121113 A091710 this_sequence A122653 A136943 A136938
Adjacent sequences: A054877 A054878 A054879 this_sequence A054881 A054882 A054883
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KEYWORD
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nonn,walk
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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