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A158677
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Period 6: repeat [3, 4, 0, 5, 6, 3].
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2
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3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0
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OFFSET
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1,1
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COMMENTS
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Also the decimal expansion of 1135210/333333 or the continued fraction of (81+sqrt(9867))/58.
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LINKS
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Table of n, a(n) for n=1..105.
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*(3+4*x+5*x^3+6*x^4+3*x^5) / ((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)).
a(n) = a(n-6) for n>6.
a(n) = (1/30)*{7*(n mod 6)+22*[(n+1) mod 6]+2*[(n+2) mod 6]-18*[(n+3) mod 6]+27*[(n+4) mod 6]+2*[(n+5) mod 6]}. [Paolo P. Lava, Mar 27 2009]
a(n) = cos(n*Pi/6)^2 * (39 - 36*cos(n*Pi/3) + 6*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 23 2016
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MAPLE
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A158677:=n->[3, 4, 0, 5, 6, 3][(n mod 6)+1]: seq(A158677(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016
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MATHEMATICA
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PadRight[{}, 120, {3, 4, 0, 5, 6, 3}] (* Harvey P. Dale, Aug 06 2013 *)
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PROG
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(MAGMA) &cat [[3, 4, 0, 5, 6, 3]^^20]; // Wesley Ivan Hurt, Jun 23 2016
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CROSSREFS
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Cf. A158674.
Sequence in context: A197809 A086230 A197485 * A337164 A105576 A105826
Adjacent sequences: A158674 A158675 A158676 * A158678 A158679 A158680
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Mar 24 2009
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EXTENSIONS
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Edited and extended by R. J. Mathar, Sep 07 2009
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STATUS
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approved
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