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A070405
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a(n) = 7^n mod 13.
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2
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1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).
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FORMULA
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a(n) = (1/132)*{24*(n mod 12)+35*[(n+1) mod 12]+57*[(n+2) mod 12]-42*[(n+3) mod 12]+46*[(n+4) mod 12]+79*[(n+5) mod 12]+2*[(n+6) mod 12]-9*[(n+7) mod 12]-31*[(n+8) mod 12]+51*[(n+9) mod 12]-20*[(n+10) mod 12]-53*[(n+11) mod 12]}, with n>=0. - Paolo P. Lava, Feb 24 2010
From R. J. Mathar, Apr 20 2010: (Start)
a(n) = a(n-1) - a(n-6) + a(n-7).
G.f.: ( -1-6*x-3*x^2+5*x^3-4*x^4-2*x^5-2*x^6 ) / ( (x-1)*(x^2+1)*(x^4-x^2+1) ). (End)
a(n) = a(n-12). - G. C. Greubel, Mar 20 2016
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MATHEMATICA
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PowerMod[7, Range[0, 90], 13] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, -1, 1}, {1, 7, 10, 5, 9, 11, 12}, 100] (* Harvey P. Dale, May 20 2014 *)
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PROG
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(Sage) [power_mod(7, n, 13) for n in range(0, 91)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n) = lift(Mod(7, 13)^n); \\ Altug Alkan, Mar 20 2016
(MAGMA) [Modexp(7, n, 13): n in [0..100]]; // Bruno Berselli, Mar 22 2016
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CROSSREFS
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Sequence in context: A122577 A180732 A266551 * A010730 A225694 A247191
Adjacent sequences: A070402 A070403 A070404 * A070406 A070407 A070408
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 12 2002
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STATUS
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approved
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