A131711 - OEIS

%I #20 Dec 12 2023 09:19:03

%S 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,

%T 8,1,0,1,2,5,2,9,0,9,8,5,8,1

%N Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.

%C Final digits of Pell numbers. First differences: 1, 1, 3, -3, 7, -9, 9, -1, -3, 3 -7, -1, 1 (cf. A131707).

%C 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).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1,0,1,0,-1,0,1).

%F 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]

%F 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

%t PadRight[{},120,{0,1,2,5,2,9,0,9,8,5,8,1}] (* _Harvey P. Dale_, Dec 29 2014 *)

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

%K nonn,easy,less

%O 0,3

%A _Paul Curtz_, Sep 14 2007