A010691 Period 2: repeat (1,10).

1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10

Offset

0,2

Comments

Regular continued fraction of (5+sqrt 35)/10. - R. J. Mathar, Nov 21 2011

Sequence is an infinite palindrome in two ways (numbers and English names): ONE, TEN, ONE, TEN, ONE, TEN, ONE, ... . - Eric Angelini, Sep 16 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = -9/2*(-1)^n + 11/2.

G.f.: (1+10*z)/(1-z^2). - Zerinvary Lajos, Feb 25 2009

a(n) = 10^n mod 11. - M. F. Hasler, Mar 10 2011

From Nicolas Bělohoubek, Nov 11 2021: (Start)

a(n) = 10/a(n-1). See also A010695.

a(n) = 11 - a(n-1). See also A010712. (End)

Maple

g:=(1+10*z)/((1-z^2)): gser:=series(g, z=0, 66): seq((coeff(gser, z, n)), n=0..65); # Zerinvary Lajos, Feb 25 2009

Mathematica

PadRight[{}, 100, {1, 10}] (* Harvey P. Dale, Aug 27 2013 *)

Prog

(Magma) [10^n mod 11: n in [0..80]]; // Vincenzo Librandi, Aug 24 2011

Crossrefs

Cf. A036117, A070341, A168429, A070367, A070392, A070404, A048271, A187466.

Sequence in context: A046148 A231933 A164915 * A288697 A343132 A287852

Adjacent sequences: A010688 A010689 A010690 * A010692 A010693 A010694

Keyword

nonn,easy,word

Author

N. J. A. Sloane

Status

approved