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A015609
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a(n) = 11*a(n-1) + 12*a(n-2).
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1
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0, 1, 11, 133, 1595, 19141, 229691, 2756293, 33075515, 396906181, 4762874171, 57154490053, 685853880635, 8230246567621, 98762958811451, 1185155505737413, 14221866068848955, 170662392826187461
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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_13. Example: a(2)=11 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJKLM are ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB, AKB, ALB and AMB. - Emeric Deutsch, Apr 01 2004
General form: k=12^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577, A015585. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
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LINKS
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FORMULA
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a(n) = 12^(n-1) - a(n-1).
G.f.: x/(1 - 11*x - 12*x^2). (End)
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MATHEMATICA
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CoefficientList[Series[x/(1-11*x-12*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{11, 12}, {0, 1}, 30] (* G. C. Greubel, Dec 30 2017 *)
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PROG
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(Sage) [lucas_number1(n, 11, -12) for n in range(0, 18)] # Zerinvary Lajos, Apr 27 2009
(Sage) [abs(gaussian_binomial(n, 1, -12)) for n in range(0, 18)] # Zerinvary Lajos, May 28 2009
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-11*x-12*x^2))) \\ G. C. Greubel, Dec 30 2017
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CROSSREFS
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Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577, A015585, A015592. - 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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