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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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 (deutsch(AT)duke.poly.edu), 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 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..900
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FORMULA
| a(n)=12^(n-1)-a(n-1). G.f.=x/(1-11x-12x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n)=(1/13)*[12^n-(-1)^n], with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 09 2008
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MATHEMATICA
| k=0; lst={k}; Do[k=12^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROG
| (Other) sage: [lucas_number1(n, 11, -12) for n in xrange(0, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
(Other) sage: [abs(gaussian_binomial(n, 1, -12)) for n in xrange(0, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
(MAGMA) [(1/13)*(12^n-(-1)^n): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
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CROSSREFS
| Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577, A015585, A015592 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A196731 A051431 A014994 * A157773 A024143 A057718
Adjacent sequences: A015606 A015607 A015608 * A015610 A015611 A015612
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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