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A131711
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Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.
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6
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0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Final digits of Pell numbers. First differences: 1, 1, 3, -3, 7, -9, 9, -1, -3, 3 -7, -1, 1 (cf. A131707).
Can be though of as 2 interlocking sequences, each of the form a(n) = a(n - 1) - a(n - 2) + a(n - 3) - a(n - 4) + a(n - 5).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,0,-1,0,1).
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FORMULA
| a(n)=(1/198)*{29*(n mod 12)+128*[(n+1) mod 12]-37*[(n+2) mod 12]+62*[(n+3) mod 12]+29*[(n+4) mod 12]-136*[(n+5) mod 12]+161*[(n+6) mod 12]-103*[(n+7) mod 12]+62*[(n+8) mod 12]-37*[(n+9) mod 12]-4*[(n+10) mod 12]-4*[(n+11) mod 12]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 02 2007
G.f.: (x^8+8x^7+4x^6+5x^4+4x^2+2x+1)x/((1-x) (1+x) (x^2+x+1) (x^2-x+1) (x^4-x^2+1)). a(n) = |A131201(n)| = A000129(n) mod 10 = A000129(n)-10*A131727(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2008]
a(n) = 25/6 -4*cos(Pi*n/6)/sqrt(3) -sqrt(3)*sin(Pi*n/6) -5*cos(Pi*n/3)/3 -5*cos(2*Pi*n/3)/3 +4*cos(5*Pi*n/6)/sqrt(3) +sqrt(3)*sin(5*Pi*n/6) -5*(-1)^n/6. - R. J. Mathar, Oct 08 2011
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PROG
| (PARI) [0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1][n%12+1] \\ Charles R Greathouse IV, Jun 02 2011
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CROSSREFS
| Sequence in context: A065223 A029621 A134349 * A131201 A070633 A119764
Adjacent sequences: A131708 A131709 A131710 * A131712 A131713 A131714
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KEYWORD
| nonn,easy,less
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Sep 14 2007
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