A131711 Period 12: repeat 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, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1

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

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: A240223 A134349 A354709 * A131201 A070633 A266256

Adjacent sequences: A131708 A131709 A131710 * A131712 A131713 A131714

Keyword

nonn,easy,less

Author

Paul Curtz, Sep 14 2007

Status

approved