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

0,6

Comments

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

Links

Table of n, a(n) for n=0..101.

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

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

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 *)

Prog

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

Crossrefs

Cf. A000035, A010872, A093719.

Sequence in context: A321755 A052314 A271606 * A278839 A348653 A278287

Adjacent sequences: A093715 A093716 A093717 * A093719 A093720 A093721

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 12 2004

Status

approved