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A015552
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a(n) = 6*a(n-1) + 7*a(n-2), a(0) = 0, a(1) = 1.
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13
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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
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OFFSET
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0,3
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COMMENTS
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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, Apr 01 2004
General form: k=7^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
The ratio a(n+1)/a(n) converges to 7 as n approaches infinity. - Felix P. Muga II, Mar 09 2014
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LINKS
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FORMULA
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a(n) = 6*a(n-1) + 7*a(n-2).
G.f.: x/(1-6*x-7*x^2).
a(n) = 7^(n-1) - a(n-1). (End)
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EXAMPLE
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G.f. = x + 6*x^2 + 43*x^3 + 300*x^4 + 2101*x^5 + 14706*x^6 + 102943*x^7 + ...
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MAPLE
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MATHEMATICA
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Table[(7^n - (-1)^n)/8, {n, 0, 30}] (* G. C. Greubel, Dec 2017 *)
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PROG
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(PARI) {a(n) = if ( n<0, 0, (7^n - (-1)^n) / 8)};
(Sage) [lucas_number1(n, 6, -7) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
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CROSSREFS
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Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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