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Search: id:A015552
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| A015552 |
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Linear 2nd order recurrence. |
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+0
8
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| 0, 1, 6, 43, 300, 2101, 14706, 102943, 720600, 5044201, 35309406, 247165843, 1730160900, 12111126301, 84777884106, 593445188743, 4154116321200, 29078814248401, 203551699738806, 1424861898171643, 9974033287201500
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of walks of length n between any two distinct nodes of the complete graph K_8. Example: a(2)=6 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGH are: ACB, ADB, AEB, AFB, AGB and AHB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
General form: k=7^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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FORMULA
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a(n) = 6 a(n-1) + 7 a(n-2).
G.f.: x/(1-6x-7x^2). a(n)=7^(n-1)-a(n-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n)=(7^n-(-1)^n)/8 [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Jul 06 2009]
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MATHEMATICA
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k=0; lst={k}; Do[k=7^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (7^n-(-1)^n)/8)
(Other) sage: [lucas_number1(n, 6, -7) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
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CROSSREFS
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Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A156676 A099322 A014989 this_sequence A091129 A091128 A025594
Adjacent sequences: A015549 A015550 A015551 this_sequence A015553 A015554 A015555
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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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