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A131711 Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1. 6
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; text; internal format)
OFFSET

0,3

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).

LINKS

Table of n, a(n) for n=0..47.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,0,-1,0,1).

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, 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, 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

MATHEMATICA

PadRight[{}, 120, {0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1}] (* Harvey P. Dale, Dec 29 2014 *)

PROG

(PARI) [0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1][n%12+1] \\ Charles R Greathouse IV, Jun 02 2011

CROSSREFS

Sequence in context: A029621 A240223 A134349 * A131201 A070633 A266256

Adjacent sequences:  A131708 A131709 A131710 * A131712 A131713 A131714

KEYWORD

nonn,easy,less

AUTHOR

Paul Curtz, Sep 14 2007

STATUS

approved

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Last modified February 22 19:30 EST 2018. Contains 299469 sequences. (Running on oeis4.)