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Search: id:A015443
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| A015443 |
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Generalized Fibonacci numbers: a(n) = a(n-1) + 8 a(n-2). |
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+0
11
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| 1, 1, 9, 17, 89, 225, 937, 2737, 10233, 32129, 113993, 371025, 1282969, 4251169, 14514921, 48524273, 164643641, 552837825, 1869986953, 6292689553, 21252585177, 71594101601, 241614783017, 814367595825, 2747285859961
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Construct a graph as follows: form the graph whose adjacency matrix is the tensor product of that of P_3 and [1,1;1,1], then add a loop at each of the extremity nodes. a(n-1) counts walks of length n between adjacent nodes. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2004
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LINKS
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Joerg Arndt, Fxtbook
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FORMULA
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a(n)={[ (1+sqrt(33))/2 ]^(n+1) - [ (1-sqrt(33))/2 ]^(n+1)}/sqrt(33).
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-8)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 1, -8) for n in xrange(1, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A015442, A015441.
Cf. A100302, A100303.
Sequence in context: A118527 A166705 A116526 this_sequence A121442 A049440 A073221
Adjacent sequences: A015440 A015441 A015442 this_sequence A015444 A015445 A015446
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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