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Search: id:A091002
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| A091002 |
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Number of walks of length n between non-adjacent nodes on the Petersen graph. |
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+0
5
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| 0, 0, 1, 2, 9, 22, 77, 210, 673, 1934, 5973, 17578, 53417, 158886, 479389, 1432706, 4309041, 12905278, 38759525, 116191194, 348748345, 1045895510, 3138385581, 9413758642, 28244072129, 84726623982, 254191056757, 762550800650
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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3^n=A091000(n)+3*A091001(n)+6*a(n). Binomial transform of A091005.
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FORMULA
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G.f.: x^2/((1-x)(1+2x)(1-3x)); a(n)=3^n/10+(-2)^n/15-1/6.
a(n)=(A000244(n)-A001045(n+1)(-1)^n-4*A001045(n)(-1)^(n+1))/10.
a(n)=sum(binomial(n-k, k)*6^(k-1), k=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 30 2006
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MAPLE
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a:=n->sum(binomial(n-k, k)*6^(k-1), k=1..n): seq(a(n), n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 30 2006
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PROGRAM
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a(-2)=0, a(-1)=0, sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 2, 1, 6, lambda n: 1) sage: [it.next() for i in xrange(0, 29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
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CROSSREFS
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Sequence in context: A023625 A166754 A026589 this_sequence A025176 A032315 A032224
Adjacent sequences: A090999 A091000 A091001 this_sequence A091003 A091004 A091005
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 12 2003
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