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A105899
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Period 6: repeat [1, 1, 2, 2, 3, 3].
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4
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1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 2
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OFFSET
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0,3
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COMMENTS
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Terms of the simple continued fraction of 82/[sqrt(25277)-111]. Decimal expansion of 3401/30303. [Paolo P. Lava, Aug 05 2009]
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LINKS
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Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).
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FORMULA
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G.f.: -(3*x^4+2*x^2+1)/(x-1)/(x^2+x+1)/(x^2-x+1). a(n) = A131555(n)+1. - R. J. Mathar, Nov 14 2007
a(n) = (1/30)*{14*(n mod 6)+4*[(n+1) mod 6]-[(n+2) mod 6]+4*[(n+3) mod 6]-[(n+4) mod 6]+4*[(n+5) mod 6]}. - Paolo P. Lava, Dec 19 2007
From Wesley Ivan Hurt, Jun 17 2016: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.
a(n) = (12-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/6. (End)
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MAPLE
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A105899:=n->(12-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/6: seq(A105899(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016
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MATHEMATICA
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Flatten[Table[{1, 1, 2, 2, 3, 3}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{}, 120, {1, 1, 2, 2, 3, 3}] (* Harvey P. Dale, May 09 2022 *)
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PROG
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(PARI) a(n)=1+n%6\2 \\ Jaume Oliver Lafont, Aug 30 2009
(MAGMA) &cat[[1, 1, 2, 2, 3, 3]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016
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CROSSREFS
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Cf. A131555.
Cf. A178308 Decimal expansion of (111+sqrt(25277))/158. [Klaus Brockhaus, May 24 2010]
Sequence in context: A288723 A071859 A135695 * A071434 A227314 A128924
Adjacent sequences: A105896 A105897 A105898 * A105900 A105901 A105902
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KEYWORD
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nonn,easy,less
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AUTHOR
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Paul Curtz, Aug 27 2007
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 15 2007
More terms from Klaus Brockhaus, May 24 2010
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STATUS
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approved
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