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A052465
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a(n) is the solution k to Mod[24k,11^n]==1.
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5
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6, 116, 721, 14031, 87236, 1697746, 10555551, 205427261, 1277221666, 24856698576, 154543821581, 3007660527691, 18699802411296, 363926923850606, 2262676091766811, 44035157785923321
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OFFSET
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1,1
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COMMENTS
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Related to a Ramanujan congruence for the partition function P.
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REFERENCES
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G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1 Issue 6, December 2014, ISSN: 2349-8862; http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..900
Eric Weisstein's World of Mathematics, Partition Function Congruences.
Index entries for linear recurrences with constant coefficients, signature (1,121,-121).
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FORMULA
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G.f.: x*(-121*x^2+110*x+6)/((1-x)*(1-121*x^2)). - Vincenzo Librandi, Jul 01 2012
a(n) = a(n-1) +121*a(n-2) -121*a(n-3). - Vincenzo Librandi, Jul 01 2012
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MATHEMATICA
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Table[PowerMod[24, -1, 11^c], {c, 20}]
CoefficientList[Series[(-121x^2+110x+6)/((1-x)(1-121*x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 01 2012 *)
LinearRecurrence[{1, 121, -121}, {6, 116, 721}, 20] (* Harvey P. Dale, Apr 27 2014 *)
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PROG
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(MAGMA) I:=[6, 116, 721]; [n le 3 select I[n] else Self(n-1)+121*Self(n-2)-121*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 01 2012
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CROSSREFS
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Cf. A052462, A052463, A052466.
Sequence in context: A317172 A278752 A003425 * A229582 A113015 A024275
Adjacent sequences: A052462 A052463 A052464 * A052466 A052467 A052468
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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