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A204671
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a(n) = n^n (mod 6).
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2
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1, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4
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OFFSET
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0,3
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COMMENTS
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For n>0, periodic with period 6 = A174824: repeat [1, 4, 3, 4, 5, 0].
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
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FORMULA
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G.f.: (x^6-5*x^5-4*x^4-3*x^3-4*x^2-x-1)/((x-1)*(x+1)*(x^2-x+1)*(x^2+x+1)). [Colin Barker, Jul 20 2012]
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = a(n-6) for n>5.
a(0) = 1, a(n) = (17 - cos(n*Pi) - 8*cos(n*Pi/3) - 8*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/6 for n>0. (End)
a(n) = A010875(A000312(n)). - Michel Marcus, Jun 27 2016
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MAPLE
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A204671:=n->[1, 4, 3, 4, 5, 0][(n mod 6)+1]: 1, seq(A204671(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016
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MATHEMATICA
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Table[PowerMod[n, n, 6], {n, 0, 140}]
Join[{1}, LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 4, 3, 4, 5, 0}, 86]] (* Ray Chandler, Aug 26 2015 *)
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PROG
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(MAGMA) [1] cat &cat [[1, 4, 3, 4, 5, 0]^^20]; // Wesley Ivan Hurt, Jun 23 2016
(PARI) a(n)=lift(Mod(n, 6)^n) \\ Andrew Howroyd, Feb 25 2018
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CROSSREFS
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Cf. A000312, A010875, A174824, A204690.
Sequence in context: A332472 A049788 A002558 * A204816 A204818 A099634
Adjacent sequences: A204668 A204669 A204670 * A204672 A204673 A204674
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KEYWORD
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nonn,easy
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AUTHOR
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José María Grau Ribas, Jan 18 2012
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STATUS
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approved
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