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Search: id:A015592
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| A015592 |
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a(n) = 10 a(n-1) + 11 a(n-2). |
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+0
3
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| 0, 1, 10, 111, 1220, 13421, 147630, 1623931, 17863240, 196495641, 2161452050, 23775972551, 261535698060, 2876892678661, 31645819465270, 348104014117971, 3829144155297680, 42120585708274481
(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_12. Example: a(2)=10 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJKL are: ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB, AKB and ALB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
General form: k=11^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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FORMULA
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a(n)=11^(n-1)-a(n-1). G.f.=x/(1-10x-11x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n)=-(1/12)*(-1)^n+(1/12)*11^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 15 2008
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MATHEMATICA
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k=0; lst={k}; Do[k=11^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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(Other) sage: [lucas_number1(n, 10, -11) for n in xrange(0, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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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 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A087545 A078252 A014993 this_sequence A122574 A084031 A066275
Adjacent sequences: A015589 A015590 A015591 this_sequence A015593 A015594 A015595
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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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