A093718 a(n) = (n mod 3)^(n mod 2).

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

Offset: 0

Author

Reinhard Zumkeller, Apr 12 2004

Keywords

• nonn
• easy

Comments

Period 6: repeat [1, 1, 1, 0, 1, 2]. - Joerg Arndt, Jun 09 2013

Links

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

Crossrefs

Cf. A000035, A010872, A093719.

Programs

Magma

&cat [[1, 1, 1, 0, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Maple

A093718:=n->(n mod 3)^(n mod 2): seq(A093718(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2014

Mathematica

Table[Mod[n + 3, 2 + Mod[n, 2]], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 16 2014 *)
LinearRecurrence[{1,-1,1,-1,1},{1,1,1,0,1},120] (* Harvey P. Dale, Jan 17 2021 *)

Formula

a(n) = A010872(n)^A000035(n).

G.f.: ( -1-x^2-2*x^4+x^3 ) / ( (x-1)*(1-x+x^2)*(1+x+x^2) ). - R. J. Mathar, Jun 09 2013

a(n) = (n + 3) mod (2 + n mod 2) - Wesley Ivan Hurt, Aug 16 2014

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) = cos(n*Pi/6) * (6*cos(n*Pi/6)-3*cos(n*Pi/2)-sqrt(3)*sin(n*Pi/2))/3.

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).

a(n) = a(n-6) for n>5. (End)

E.g.f.: cosh(x) - cosh(x/2)*sin(sqrt(3)*x/2)/sqrt(3) + cos(sqrt(3)*x/2)*sinh(x/2) + sinh(x). - Stefano Spezia, Jul 26 2024