A152857 Period 5: repeat [0, 2, 3, 0, 0].

0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0, 0, 2, 3, 0, 0

Offset

0,2

Links

Table of n, a(n) for n=0..69.

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

Formula

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

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

a(n) = 1+(-1/2-1/10*5^(1/2))*cos(2*n*Pi/5)+(1/10*(3*(5-5^(1/2))^(1/2)+2*(5+5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(1/10*5^(1/2)-1/2)*cos(4*n*Pi/5)+(1/10*(2*(5-5^(1/2))^(1/2)-3*(5+5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5).

a(n) = (5 + 4*cos(2*(n-1)*Pi/5) + 4*cos(4*(n-1)*Pi/5) + 6*cos(2*(n+3)*Pi/5) + 6*cos(4*(n+3)*Pi/5))/5. - Wesley Ivan Hurt, Jun 25 2022

Mathematica

PadRight[{}, 100, {0, 2, 3, 0, 0}] (* Harvey P. Dale, Aug 09 2021 *)

Crossrefs

Cf. A026045.

Sequence in context: A048735 A102037 A286530 * A097946 A083926 A218757

Adjacent sequences: A152854 A152855 A152856 * A152858 A152859 A152860

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved