A158674 -id:A158674 - cp's OEIS frontend

A158677 Period 6: repeat [3, 4, 0, 5, 6, 3].

3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0, 5, 6, 3, 3, 4, 0

Offset: 1

Paul Curtz, Mar 24 2009

Also the decimal expansion of 1135210/333333 or the continued fraction of (81+sqrt(9867))/58.

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

Cf. A158674.

&cat [[3, 4, 0, 5, 6, 3]^^20]; // Wesley Ivan Hurt, Jun 23 2016

A158677:=n->[3, 4, 0, 5, 6, 3][(n mod 6)+1]: seq(A158677(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

PadRight[{}, 120, {3,4,0,5,6,3}] (* Harvey P. Dale, Aug 06 2013 *)

G.f.: x*(3+4*x+5*x^3+6*x^4+3*x^5) / ((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)).
a(n) = a(n-6) for n>6.
a(n) = cos(n*Pi/6)^2 * (39 - 36*cos(n*Pi/3) + 6*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 23 2016

Edited and extended by R. J. Mathar, Sep 07 2009

A158678 Period 18: repeat 0,0,0,3,0,0,0,3,0,-3,0,3,0,-3,0,0,0,-3.

Original entry on oeis.org

0, 0, 0, 3, 0, 0, 0, 3, 0, -3, 0, 3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 3, 0, -3, 0, 3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 3, 0, -3, 0, 3, 0, -3, 0, 0, 0, -3

Offset: 1

Paul Curtz, Mar 24 2009

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

Cf. A158674, A158677.

a(n) = A158674(n) - A158677(n) = a(n-18).
G.f.: 3*(1+x+x^2)*(x^2-x+1)*(x^4-x^2+1)*x^4/((x^6-x^3+1)*(x^6+x^3+1)). - R. J. Mathar, Apr 08 2009
a(n) = - a(n-6) - a(n-12) for n > 12. - Chai Wah Wu, Feb 18 2021

Edited by R. J. Mathar, Apr 08 2009

cp's OEIS Frontend

A158677 Period 6: repeat [3, 4, 0, 5, 6, 3].

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