A152855 Period 5: Repeat [1, 2, 0, 2, 0].

1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0

Offset

0,2

Links

Table of n, a(n) for n=0..104.

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

Formula

a(n+5) = a(n) with a(0) = 1, a(1) = a(3) = 2 and a(2) = a(4) = 0.

O.g.f.: f(z) = (1+2*z+2*z^3)/(1-z^5).

a(n) = 1+(-1/5*((5-5^(1/2))^(1/2)-(5+5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(1/5*((5-5^(1/2))^(1/2)+(5+5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5).

Mathematica

PadRight[{}, 120, {1, 2, 0, 2, 0}] (* Harvey P. Dale, Dec 17 2022 *)

Crossrefs

Cf. A026039.

Sequence in context: A174793 A245718 A192011 * A218907 A192575 A029401

Adjacent sequences: A152852 A152853 A152854 * A152856 A152857 A152858

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved