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Search: id:A054877
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| A054877 |
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Closed walks of length n along the edges of a pentagon based at a vertex. |
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+0
3
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| 1, 0, 2, 0, 6, 2, 20, 14, 70, 72, 254, 330, 948, 1430, 3614, 6008, 13990, 24786, 54740, 101118, 215766, 409640, 854702, 1652090, 3396916, 6643782, 13530350, 26667864, 53971350, 106914242, 215492564, 428292590, 860941798
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In general a(n,m)=2^n/m*Sum(k,0,m-1,Cos(2Pi*k/m)^n) counts closed walks of length n at a vertex of the cyclic graph on m nodes C_m. Here we have the case m=5. - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
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FORMULA
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G.f.: -1/5*1/(2*x-1)-2/5*(2+x)/(x^2-x-1). a(n)=( 2^n + 2*(-1)^n*( F(n) + F(n-2) ) )/5, for n>1, where F(n) is the n-th Fibonacci number (cf. A000045)
a(n)=2^n/5*Sum(k, 0, 4, Cos(2Pi*k/5)^n) - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
Recurrence: a(n)=5(a(n-2)-a(n-4)) + 2a(n-5) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 04 2004
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CROSSREFS
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{a(n)/2} for n>1 is A052964.
Sequence in context: A078991 A021833 A049257 this_sequence A095834 A106828 A055302
Adjacent sequences: A054874 A054875 A054876 this_sequence A054878 A054879 A054880
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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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